Research ArticleAnalysis of the Structural Characteristics of the Online SocialNetwork of Chinese Professional Athletes

Yue Wang 1 Qian Huang 1 Qiurong Wang 1 Yang Xun 2 Yujiao Tan 1

Shuqin Cui 3 Linxiao Ma3 Penglin Huang 4 Meijuan Cao 1 and Bin Zhang 1

1Xirsquoan Physical Education University Xirsquoan 710065 China2School of Economics and Finance Xirsquoan Jiaotong University Xirsquoan 710049 China3Sport College Xirsquoan University of Architecture and Technology Xirsquoan 710311 China4Shandong Sport University Jinan 250063 China

Correspondence should be addressed to Qian Huang huangqian168126com

Received 9 October 2020 Revised 16 January 2021 Accepted 8 February 2021 Published 19 February 2021

Academic Editor Hongshu Chen

Copyright copy 2021 Yue Wang et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In response to the lack of research on the online social network structure of athletes elements of research on the online social networkstructure of athletes were constructed based on the whole network perspective and through the study of the characteristics of thewhole online social network structure of athletes in order to provide reference for the physical and mental health development ofathletes from a new perspective Data were collected through questionnaires and several software programs were used to preprocessand analyse the collected data +rough the analysis of the online whole network structure it was found that the network density ofthe online support network was generally greater than that of the online discussion network and athletes still showed strongerpractical support demands and behaved more rationally in the process of training and learning life while from the perspective of therelationship structure the athletesrsquo family and classmatesrsquo online support is weaker than that in previous studies in terms of the wholenetwork strong relationships still dominate in this population while attention should be paid to the impact of weak relationships

1 Introduction

Chinarsquos competitive sports implement the ldquoone piece ofmindrdquo ldquoone organizationrdquo and ldquoconsistent trainingrdquotraining system and athletes are in a relatively independentand closed environment for a long time +e traininglearning and living environment of athletes is relativelyindependent and closed for a long time and the breadthdepth and integration of real social interaction are subject tocertain limitations [1ndash5] With the rapid development of theInternet online social network platforms such as WeChatWeibo QQ and social networking sites have been integratedinto peoplersquos daily lives and the huge Internet user base hasformed an intricate virtual society-Online Social Network

(OSN) [6ndash14] which provides athletes with a more modernand diverse way to socialize [15ndash17]

Athletes in particular Chinese competitive athletes havevery specific social relationships +e offline social rela-tionships of athletes described in this article are relativelyclosed ie closed for a certain amount of time and closed fora certain amount of space+e reality is that athletes trainingin preparation for an event for example will remain in oneor several relatively closed environments for a period of time(eg weeks or even months) and connections to the outsideworld are negligible compared to the large number of in-ternal connections Due to the influence of offline socialinteraction this group is also relatively closed onlinecompared to the general public

HindawiComplexityVolume 2021 Article ID 6647664 10 pageshttpsdoiorg10115520216647664

Online social networks are having an increasing impacton athletesrsquo social support and social inclusion as athleteslearn about society access information express their aspi-rations and have greater emotional resonance through theInternet [18]

Due to the special nature of athletesrsquo social relationshipsonline social networking has become an important way forathletes to connect with others +e survey data shows thatathletesrsquo social networks are limited in time and spacecompared to those of the general public in that their onlinetime is relatively limited and fixed and their online activitiesare relatively concentrated +e challenge in studying thisonline social network of this population is that online data isnot easy to collect and there is a lack of references so wecontinue to use traditional questionnaires+e innovation ofthis paper is to conduct an online social support networkstudy based on the previous offline social support networkwhich is an exploratory approach to fill the gap in this field inChina and is groundbreaking in terms of both the athletepopulation and the research methodology

Current research on athletesrsquo social networks focuses onthe attribute variables and structural analysis of real socialnetworks and their online social data and research arelacking Athletesrsquo online social network is an open andcomplex system a large-scale collection consisting of con-nected relationships between athletes and other networkcitizens including teammates coaches family membershometown friends and even strangers [19 20] +inkingabout and understanding athletesrsquo online social structurefrom different dimensions and studying the inner laws ofprofessional athletesrsquo network behaviour at multiple levels(micro- meso- and macrolevel) can help grasp the mech-anisms of athletesrsquo behavioural patterns and provide refer-ences for improving their online social support networkspromoting social integration and further improving thesports system

Online social networks are an extension of social net-works [21 22] a form of social networks existing in anotherspace and their structural characteristics can be analysed byapplying the methods of social network analysis Accordingto the different boundaries of social networks the study ofsocial network structure is divided into two directions in-dividual networks and whole networks [23 24] Individualnetworks locate the network with individuals as the centreand the individual characteristics and behavioural conceptsof concern while whole networks consist of a set of specificindividuals and the interrelationships between them and thenetwork members have relatively obvious boundaries[25ndash27] +e network as a whole exhibits a certain structureand has an impact on the actors within it [28] In otherwords the ldquostructuralistrdquo perspective of ldquosocial structurerdquoinfluences the ldquodynamic rolerdquo +is study examines thestructural characteristics of athletesrsquo whole online socialnetwork by collecting online data from athletes in order toprovide a new perspective on athletesrsquo physical and mentalhealth development

2 Elements of Athletesrsquo Online Social Structure

+e term ldquoonline social networkrdquo refers to the network ofsocial users in the Internet [29] According to the EU studyon social computing online social networks can be dividedinto four categories instant messaging (WeChat QQ etc)online social networking (Facebook Renren etc) micro-blogging (Twitter Weibo etc) and shared space (forumsblogs etc) +e latest data released by CNNIC shows thatapplications such asWeChat short video and live streamingare increasingly integrated with the lives of Chinese Internetusers In the preliminary stage of this study a sample of 451athletes were surveyed on online social network applica-tions and the most frequently used application by re-spondents was instant messaging accounting for 931 ofwhich WeChat had the highest usage rate

As shown in Figure 1 online social network for athletesconsists of two categories social support network and socialdiscussion network [23 30] +e online social supportnetwork is based on the Van der Poole social supportclassification method and it is divided into social onlinesupport emotional online support achievement onlinesupport and practical online support Based on the Instituteof Population and Development of Xirsquoan Jiaotong Uni-versityrsquos social network of migrant workers and the socialnetwork of athletes under Huang Qianrsquos complex networkthe online social discussion network is analysed [23 31]from four aspects employment online discussion revenueonline discussion professional online discussion and loveand marriage online discussion +e questionnaire data arecollected by positioning method

3 Data Collection

Whole social networks require closed groups and suchsociologically significant networks are generally not large insize +is study sampled a closed group formed by 147professional taekwondo athletes from the Shaanxi Boxingand Taekwondo Sports Management Centre +e ques-tionnaire was divided into two parts the first part investi-gated the basic information of the athletes including genderdate of birth and total number of WeChat friends and thesecond part designed a list of 147 athletesrsquo names and codenames according to the roster method [32 33]

+e data collection was conducted from January 10 toJanuary 13 2020 To ensure accurate and valid data theauthor interpreted the questions on site and in the secondpart of the questionnaire filling athletes first filled in theirown code names according to the code name list and thenselected other athletes who had correspondence with themin the test questions item by item and filled in their cor-responding code names +rough a survey of coaches andrelevant researchers and drawing on Huang Qian et alrsquosanalysis of athletesrsquo whole social networks [3 4] the fol-lowing measurement questions about athletesrsquo online socialnetworks were selected (1) Who do you interact with on

2 Complexity

online platforms (conversations holiday greetings filetransfers etc) (2) In online chats to whom do you confideyour feelings (3) Who do you turn to for help with smalldaily tasks on online platforms (including online adviceonline payments) (4) Who are the people who push in-formation online (private messages group notifications orsharing with friends) that would be helpful to your training(5) Who would you like to talk to online about issues relatedto training or sports teammanagement etc (6) Who wouldyou like to discuss marriage topics with online (7) Whowould you like to discuss employment issues with online (8)With whom would you like to discuss issues such as incomeonline Respondents ticked each item according to the listand the relationship was recorded as ldquo1rdquo if selected and ldquo0rdquootherwise Eight relationship matrices consisting of ldquo0rdquo andldquo1rdquo are formed for example in Table 1 +e questionnaireswere collected on site and four athletes were away fortraining during the collection period so the authorinstructed them to complete the questionnaires online viathe Internet After the questionnaires were collected theldquoinformantsrdquo were used to understand the general situationof the training team and the questionable data was returnedto the author 147 valid questionnaires were collected In thispaper the data cleaning and two-party relationship datastatistics are done by self-programmed Excel VBA whileother characteristic index calculation and topology drawingare processed by Ucinet and Gephi software

To illustrate the relationship matrix for athletes using anonline practical support network as an example it is suf-ficient to intercept parts of the matrix that illustrate theproblem as it is large In Table 1 N represents the totalnumber of nodes and ai (i 12 20) denote athlete nodesand due to space limitations only a1 to a20 are taken Usingformula (1) to calculate its density which is only 00273 wecan find that the matrix is a sparse matrix (L represents theactual number of connections N 147 is the number ofnodes generally less than 005 is considered as a sparsematrix) in line with the basic characteristics of social net-works secondly the distribution of connections has no

obvious regularity (ie nondiagonal array triangular arrayunit array etc) which is a random network Other thematicnetworks BsimH are similar

d(G) L

N(N minus 1) (1)

4 Analysis of the Characteristics of WholeOnline Social Network

41 Topology of Athletes Network In order to visualise therelationship structure of the eight online social networks forathletes the online social network topology diagram [34ndash36]was drawn using Gephi as shown in Figure 2 with each ofthe eight subgraphs labelled with the letters A-H In eachdirected graph the arrow indicates the direction of therelationship eg a23 points to a8 in subgraph B whichmeans that xm23 is willing to confide in xm8 about what ison his mind +ese eight subnetworks are derived from theeight relationship matrices A to H collated through thequestionnaire as isomorphic to Table 1

As can be seen the online practical support network isthe most densely connected and all nodes are connectedto each other indicating that athletes are most sociallyactive and connected online +e practical online supportnetwork is also denser with no isolated points +eemotional online support employment online discus-sion achievement online support revenue online dis-cussion professional online discussion and love andmarriage online discussion networks all have isolatedpoints especially the love and marriage online discussionnetworks which have the sparsest relationships the mostisolated points and multiple subnetworks that are notconnected to each other

42 Network Viscosity Network viscosity reflects the degreeof overall network node association and overall cohesionand is measured by network density and network distance

Online social network for athletes

Online social supportnetwork for athletes

Online social discussionnetwork for athletes

Social online support

Emotional online support

Achievement online support

Practical online support

Employment online discussion

Revenue online discussion

Professional online discussion

Love and marriage online discussion

Figure 1 Organization structure of social network of athletes

Complexity 3

Table 1 Athlete online relationship matrix

N a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a8 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a9 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 a10 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a12 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 a13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 a15 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 a16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 a17 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 a18 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 a19 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 a20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

(a) (b)

(c) (d)

Figure 2 Continued

4 Complexity

Network density is an important metric in the structuralform of a network and is defined as the ratio of the numberof edges actually present in the network to the maximumnumber of edges that can be accommodated Networkdensity is commonly used in online social networks tomeasure the density of social relationships with higherdensity indicating more connections and the greater effec-tiveness of the networkrsquos influence on nodes +e networkdistance is used to describe the length of the shortest pathbetween nodes and the clustering coefficient reflects thedegree of network aggregation +e combination of networkdistance and clustering coefficient can demonstrate theldquosmall worldrdquo effect showing how nodes are embedded intheir surrounding nodes By referring to relevant researchresults [37ndash39] an indicator is proposed here to combine thetwo as shown in (2) and the last column of Cd is obtained asin Table 2 the higher the Cd the more obvious the ldquosmallworldrdquo effect

Cdi ci1113936ici + di1113936idi( 1113857

2 (2)

Statistics on the whole network viscosity character-istics of the athletesrsquo online social networks are shown inTable 2 +e network density of each of the athletesrsquoonline social networks was in the interval [0016 0028]indicating that the network had essentially equal influ-ence on the athletes Among the online social supportnetworks emotional online support was the most lackingand their network density was only 0016 among theonline social discussion networks the athletes were moreconcerned with income issues Comparing the averagedistance of the networks revealed that athletes had thelongest chain of online practical support relationshipsand were prone to extend online practical support re-lationships +e average clustering coefficient for love andmarriage online discussions was only 03 with the

(e) (f )

(g) (h)

Figure 2 Topology of the online social network (a) Practical online support network (b) Emotional online support network (c) Socialonline support network (d) Employment online discussion network (e) Achievement online support network (f ) Revenue onlinediscussion network (g) Professional online discussion network (h) Love and marriage online discussion network

Complexity 5

sparsest network relationships +e ldquosmall worldrdquo effectof practical online support network is most evident in theCd measure

43Centrality Centrality measures the structural propertiesof social networks at a microlevel and is usually measured bythree indicators degree centrality closeness centrality andbetweenness centrality

As shown in (3) g represents the size of the network anddegree centrality CD is the most direct indicator of thecentrality of a network node it measures the total number ofdirect links between a node and other nodes +e higher thedegree centrality is the more important the node is in thenetwork in the case of directed graphs the two parametersout-degree and in-degree need to be considered

CD Ni( 1113857 1113944

g

j1xij

CDprime Ni( 1113857

CD Ni( 1113857

g minus 1 ine j

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Closeness centrality C(x) examines the extent to which anode propagates information without relying on other nodesif a node is at a short distance from all other nodes then thatpoint is at the overall centre As shown in (4) d(x y) indicatesthe distance between node x and node y

C(x) 1

1113936yd(y x) (4)

As shown in (4) betweenness centrality characterises theextent to which a node is known as a bridge to the variousothers or the extent to which it can control others σst(v)

denotes the number of shortest paths of two nodes throughpoint v and σst denotes the total number of shortest paths oftwo nodes

CB(v) 1113944sne vne t

σst(v)

σst

(5)

+e data was processed using the formulae above +echaracteristics of the whole online social network structureof the athletes in-degree and out-degree are shown in Ta-ble 3 +e maximum values show that the out-degree is

generally greater than the in-degree indicating that athletesactively seek online support and online discussionmore thanthey passively receive it +e minimum value of in-degreeand out-degree for all networks is 0 indicating that there areathletes who do not engage in online support and onlinediscussion behaviours with others in their sport team Inaddition there is more variation between individual athletessuch as the practical online support network and achieve-ment online support networks which have a maximumvalue of 25 while both have a minimum value of 0

Table 4 shows the parameter values for the whole onlinesocial network centrality characteristics of the athletesComparing the indicators of eccentricity closeness cen-trality harmonic centrality and betweenness centrality re-veals that athletes have a preference for seeking achievementsupport over other online support Online social discussionand online social support in general show a more active andactive search for support and discussion while acceptance ismore passive In terms of the propagation of online socialsupport and online social discussion relationships athleteswere more likely to extend their daily help support rela-tionships and were susceptible to the influence ofintermediaries Overall the higher closeness centrality oflove and marriage online discussion network indicates ahigher chance of connection between nodes Harmoniccentrality is usually for nonconnected networks and can beignored here Network with higher betweenness centralityindicates that more nodes in the network play a role inconnecting these groups together such as practical onlinesupport network

44 Bipartite Relationship Tripartite Relationship Bipartiterelationship is the basic unit of statistical analysis of socialnetworks For directed networks the bipartite relationshipbetween two nodes in the network includes reciprocal re-lationships one-way relationships and nulls

Tripartite relationships ie relationships between threenodes are formed by combining three pairs of bipartiterelationships +e tripartite structure is the basis of socialstructure and is described by scholars such as Holland as 16isomorphic categories each represented by three or foursymbols the first number represents the number of recip-rocal tripartite relations the second number represents thenumber of asymmetrical tripartite relations the thirdnumber represents the number of nulls in tripartite

Table 2 +e viscosity characteristics of online social network

Name of network Density Mean distance Average clustering coefficientPractical online support network 0028 5663 0401Emotional online support network 0017 4025 0310Social online support network 0024 4672 0361Employment online discussion network 0016 3138 0314Achievement online support network 002 2781 0379Revenue online discussion network 0021 3059 0388Professional online discussion network 0019 2911 0388Love and marriage online discussion network 0016 2967 03

6 Complexity

relations and if there is a final letter it is used to distinguishbetween two similar tripartite relations (T for transmissionC for circular U for up and D for down)

+e overall number of relationships between the 147nodes in this study totalled 3668 and Tables 5 and 6 showthe proportion of each relationship to the overall relation-ship in the bipartite and tripartite relationships respectivelyIt can be seen that the athlete group has an absolute majorityproportion of the nulls in all 8 networks +e proportion ofone-way relationships is very small while the proportion ofreciprocal relationships is even smaller +is suggests thatonline one-way communication between groups of athletesis rare and two-way interaction is more difficult Examiningthe actual situation based on the training patterns of theathletes this is not unrelated to the regulation of commu-nication tools A comparison of the bipartite relationshipdata reveals that athletes interact with each other mainlythrough social online support network to enhance com-munication with each other but less in terms of marriageand emotions which may be that athletes are close to eachother before they engage in emotional confessions anddiscussions on topics such as marriage

+e very large percentage of 003 in the athletesrsquo tripartiterelationships suggests that in most cases there are no onlinesupport and online discussion relationships between two outof three people in the athletesrsquo group 012 had the secondhighest proportion indicating that a larger proportion of theonline relationships among the three athletes of which onlytwo had relationships with each other were difficult totransmit among the three and that it was difficult to com-municate and collide their perceptions effectively 300 and030C had the smallest proportion of both indicating that a

small proportion of the three athletes had one-way trans-mission relationships and two-way transmission relation-ships ie the whole online social network of athletes has apoor sense of identity and belonging in the group Bipartiterelationships are the simplest relationships to consider andtripartite relationships have complex social relationshipattributes and so are generally of greater concern

45 Community Structure Realistic social networks areoften not evenly distributed but consist of many subnet-works with high similarity of nodes within the subnetworkand low similarity of nodes outside the subnetworkresulting in a community structure +e modularity Q isused to quantify or judge the merit of community division ina network as shown in (6) It is defined as the ratio of thetotal number of edges within the community to the totalnumber of edges in the network minus an expectation valuethat is the magnitude of the ratio of the total number of edgeswithin the community to the total number of edges in thenetwork that would result from the same community as-signment if the network was set as a random network If Q isgreater than 03 then the network has a significant com-munity structure [40]

Q 1113944i

eii minus a2i1113872 1113873 1113944

i

eii minus 1113944i

a2i Tre minus e

2 (6)

Figure 3 shows the modularity of the online socialsupport network and the online social discussion network Itcan be seen that the modularity Q of both is even more than08 It indicates that community structure exists widely in

Table 3 Characteristics of the whole online social network structure of athletes

NameOut-degree In-degree

Mean Std Max Min Mean Std Max MinPractical online support network 4068 3362 25000 0000 4068 1925 10000 0000Emotional online support network 2433 1880 10000 0000 2433 1537 6000 0000Social online support network 3418 3055 14000 0000 3411 1863 8000 0000Employment online discussion network 2092 2238 15000 0000 2092 1444 7000 0000Achievement online support network 2837 3384 25000 0000 2837 1869 9000 0000Revenue online discussion network 2936 2550 15000 0000 2957 1808 8000 0000Professional online discussion network 2716 2358 14000 0000 2752 1657 7000 0000Love and marriage online discussion network 2015 1728 9000 0000 2015 1468 8000 0000

Table 4 Central characteristics of the whole online social network structure of athletes

Name Eccentricity Closeness centrality Harmonic centrality Betweenness centralityPractical online support network 8247 0294 0368 251397Emotional online support network 4376 0435 0502 57780Social online support network 5266 0366 0440 129133Employment online discussion network 3092 0436 0491 21084Achievement online support network 2823 0497 0558 17440Revenue online discussion network 3832 0450 0528 28336Professional online discussion network 3694 0453 0531 20667Love and marriage online discussion network 2718 0550 0607 15389

Complexity 7

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

online platforms (conversations holiday greetings filetransfers etc) (2) In online chats to whom do you confideyour feelings (3) Who do you turn to for help with smalldaily tasks on online platforms (including online adviceonline payments) (4) Who are the people who push in-formation online (private messages group notifications orsharing with friends) that would be helpful to your training(5) Who would you like to talk to online about issues relatedto training or sports teammanagement etc (6) Who wouldyou like to discuss marriage topics with online (7) Whowould you like to discuss employment issues with online (8)With whom would you like to discuss issues such as incomeonline Respondents ticked each item according to the listand the relationship was recorded as ldquo1rdquo if selected and ldquo0rdquootherwise Eight relationship matrices consisting of ldquo0rdquo andldquo1rdquo are formed for example in Table 1 +e questionnaireswere collected on site and four athletes were away fortraining during the collection period so the authorinstructed them to complete the questionnaires online viathe Internet After the questionnaires were collected theldquoinformantsrdquo were used to understand the general situationof the training team and the questionable data was returnedto the author 147 valid questionnaires were collected In thispaper the data cleaning and two-party relationship datastatistics are done by self-programmed Excel VBA whileother characteristic index calculation and topology drawingare processed by Ucinet and Gephi software

To illustrate the relationship matrix for athletes using anonline practical support network as an example it is suf-ficient to intercept parts of the matrix that illustrate theproblem as it is large In Table 1 N represents the totalnumber of nodes and ai (i 12 20) denote athlete nodesand due to space limitations only a1 to a20 are taken Usingformula (1) to calculate its density which is only 00273 wecan find that the matrix is a sparse matrix (L represents theactual number of connections N 147 is the number ofnodes generally less than 005 is considered as a sparsematrix) in line with the basic characteristics of social net-works secondly the distribution of connections has no

obvious regularity (ie nondiagonal array triangular arrayunit array etc) which is a random network Other thematicnetworks BsimH are similar

d(G) L

N(N minus 1) (1)

4 Analysis of the Characteristics of WholeOnline Social Network

41 Topology of Athletes Network In order to visualise therelationship structure of the eight online social networks forathletes the online social network topology diagram [34ndash36]was drawn using Gephi as shown in Figure 2 with each ofthe eight subgraphs labelled with the letters A-H In eachdirected graph the arrow indicates the direction of therelationship eg a23 points to a8 in subgraph B whichmeans that xm23 is willing to confide in xm8 about what ison his mind +ese eight subnetworks are derived from theeight relationship matrices A to H collated through thequestionnaire as isomorphic to Table 1

As can be seen the online practical support network isthe most densely connected and all nodes are connectedto each other indicating that athletes are most sociallyactive and connected online +e practical online supportnetwork is also denser with no isolated points +eemotional online support employment online discus-sion achievement online support revenue online dis-cussion professional online discussion and love andmarriage online discussion networks all have isolatedpoints especially the love and marriage online discussionnetworks which have the sparsest relationships the mostisolated points and multiple subnetworks that are notconnected to each other

42 Network Viscosity Network viscosity reflects the degreeof overall network node association and overall cohesionand is measured by network density and network distance

Online social network for athletes

Online social supportnetwork for athletes

Online social discussionnetwork for athletes

Social online support

Emotional online support

Achievement online support

Practical online support

Employment online discussion

Revenue online discussion

Professional online discussion

Love and marriage online discussion

Figure 1 Organization structure of social network of athletes

Complexity 3

Table 1 Athlete online relationship matrix

N a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a8 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a9 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 a10 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a12 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 a13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 a15 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 a16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 a17 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 a18 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 a19 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 a20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

(a) (b)

(c) (d)

Figure 2 Continued

4 Complexity

Network density is an important metric in the structuralform of a network and is defined as the ratio of the numberof edges actually present in the network to the maximumnumber of edges that can be accommodated Networkdensity is commonly used in online social networks tomeasure the density of social relationships with higherdensity indicating more connections and the greater effec-tiveness of the networkrsquos influence on nodes +e networkdistance is used to describe the length of the shortest pathbetween nodes and the clustering coefficient reflects thedegree of network aggregation +e combination of networkdistance and clustering coefficient can demonstrate theldquosmall worldrdquo effect showing how nodes are embedded intheir surrounding nodes By referring to relevant researchresults [37ndash39] an indicator is proposed here to combine thetwo as shown in (2) and the last column of Cd is obtained asin Table 2 the higher the Cd the more obvious the ldquosmallworldrdquo effect

Cdi ci1113936ici + di1113936idi( 1113857

2 (2)

Statistics on the whole network viscosity character-istics of the athletesrsquo online social networks are shown inTable 2 +e network density of each of the athletesrsquoonline social networks was in the interval [0016 0028]indicating that the network had essentially equal influ-ence on the athletes Among the online social supportnetworks emotional online support was the most lackingand their network density was only 0016 among theonline social discussion networks the athletes were moreconcerned with income issues Comparing the averagedistance of the networks revealed that athletes had thelongest chain of online practical support relationshipsand were prone to extend online practical support re-lationships +e average clustering coefficient for love andmarriage online discussions was only 03 with the

(e) (f )

(g) (h)

Figure 2 Topology of the online social network (a) Practical online support network (b) Emotional online support network (c) Socialonline support network (d) Employment online discussion network (e) Achievement online support network (f ) Revenue onlinediscussion network (g) Professional online discussion network (h) Love and marriage online discussion network

Complexity 5

sparsest network relationships +e ldquosmall worldrdquo effectof practical online support network is most evident in theCd measure

43Centrality Centrality measures the structural propertiesof social networks at a microlevel and is usually measured bythree indicators degree centrality closeness centrality andbetweenness centrality

As shown in (3) g represents the size of the network anddegree centrality CD is the most direct indicator of thecentrality of a network node it measures the total number ofdirect links between a node and other nodes +e higher thedegree centrality is the more important the node is in thenetwork in the case of directed graphs the two parametersout-degree and in-degree need to be considered

CD Ni( 1113857 1113944

g

j1xij

CDprime Ni( 1113857

CD Ni( 1113857

g minus 1 ine j

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Closeness centrality C(x) examines the extent to which anode propagates information without relying on other nodesif a node is at a short distance from all other nodes then thatpoint is at the overall centre As shown in (4) d(x y) indicatesthe distance between node x and node y

C(x) 1

1113936yd(y x) (4)

As shown in (4) betweenness centrality characterises theextent to which a node is known as a bridge to the variousothers or the extent to which it can control others σst(v)

denotes the number of shortest paths of two nodes throughpoint v and σst denotes the total number of shortest paths oftwo nodes

CB(v) 1113944sne vne t

σst(v)

σst

(5)

+e data was processed using the formulae above +echaracteristics of the whole online social network structureof the athletes in-degree and out-degree are shown in Ta-ble 3 +e maximum values show that the out-degree is

generally greater than the in-degree indicating that athletesactively seek online support and online discussionmore thanthey passively receive it +e minimum value of in-degreeand out-degree for all networks is 0 indicating that there areathletes who do not engage in online support and onlinediscussion behaviours with others in their sport team Inaddition there is more variation between individual athletessuch as the practical online support network and achieve-ment online support networks which have a maximumvalue of 25 while both have a minimum value of 0

Table 4 shows the parameter values for the whole onlinesocial network centrality characteristics of the athletesComparing the indicators of eccentricity closeness cen-trality harmonic centrality and betweenness centrality re-veals that athletes have a preference for seeking achievementsupport over other online support Online social discussionand online social support in general show a more active andactive search for support and discussion while acceptance ismore passive In terms of the propagation of online socialsupport and online social discussion relationships athleteswere more likely to extend their daily help support rela-tionships and were susceptible to the influence ofintermediaries Overall the higher closeness centrality oflove and marriage online discussion network indicates ahigher chance of connection between nodes Harmoniccentrality is usually for nonconnected networks and can beignored here Network with higher betweenness centralityindicates that more nodes in the network play a role inconnecting these groups together such as practical onlinesupport network

44 Bipartite Relationship Tripartite Relationship Bipartiterelationship is the basic unit of statistical analysis of socialnetworks For directed networks the bipartite relationshipbetween two nodes in the network includes reciprocal re-lationships one-way relationships and nulls

Tripartite relationships ie relationships between threenodes are formed by combining three pairs of bipartiterelationships +e tripartite structure is the basis of socialstructure and is described by scholars such as Holland as 16isomorphic categories each represented by three or foursymbols the first number represents the number of recip-rocal tripartite relations the second number represents thenumber of asymmetrical tripartite relations the thirdnumber represents the number of nulls in tripartite

Table 2 +e viscosity characteristics of online social network

Name of network Density Mean distance Average clustering coefficientPractical online support network 0028 5663 0401Emotional online support network 0017 4025 0310Social online support network 0024 4672 0361Employment online discussion network 0016 3138 0314Achievement online support network 002 2781 0379Revenue online discussion network 0021 3059 0388Professional online discussion network 0019 2911 0388Love and marriage online discussion network 0016 2967 03

6 Complexity

relations and if there is a final letter it is used to distinguishbetween two similar tripartite relations (T for transmissionC for circular U for up and D for down)

+e overall number of relationships between the 147nodes in this study totalled 3668 and Tables 5 and 6 showthe proportion of each relationship to the overall relation-ship in the bipartite and tripartite relationships respectivelyIt can be seen that the athlete group has an absolute majorityproportion of the nulls in all 8 networks +e proportion ofone-way relationships is very small while the proportion ofreciprocal relationships is even smaller +is suggests thatonline one-way communication between groups of athletesis rare and two-way interaction is more difficult Examiningthe actual situation based on the training patterns of theathletes this is not unrelated to the regulation of commu-nication tools A comparison of the bipartite relationshipdata reveals that athletes interact with each other mainlythrough social online support network to enhance com-munication with each other but less in terms of marriageand emotions which may be that athletes are close to eachother before they engage in emotional confessions anddiscussions on topics such as marriage

+e very large percentage of 003 in the athletesrsquo tripartiterelationships suggests that in most cases there are no onlinesupport and online discussion relationships between two outof three people in the athletesrsquo group 012 had the secondhighest proportion indicating that a larger proportion of theonline relationships among the three athletes of which onlytwo had relationships with each other were difficult totransmit among the three and that it was difficult to com-municate and collide their perceptions effectively 300 and030C had the smallest proportion of both indicating that a

small proportion of the three athletes had one-way trans-mission relationships and two-way transmission relation-ships ie the whole online social network of athletes has apoor sense of identity and belonging in the group Bipartiterelationships are the simplest relationships to consider andtripartite relationships have complex social relationshipattributes and so are generally of greater concern

45 Community Structure Realistic social networks areoften not evenly distributed but consist of many subnet-works with high similarity of nodes within the subnetworkand low similarity of nodes outside the subnetworkresulting in a community structure +e modularity Q isused to quantify or judge the merit of community division ina network as shown in (6) It is defined as the ratio of thetotal number of edges within the community to the totalnumber of edges in the network minus an expectation valuethat is the magnitude of the ratio of the total number of edgeswithin the community to the total number of edges in thenetwork that would result from the same community as-signment if the network was set as a random network If Q isgreater than 03 then the network has a significant com-munity structure [40]

Q 1113944i

eii minus a2i1113872 1113873 1113944

i

eii minus 1113944i

a2i Tre minus e

2 (6)

Figure 3 shows the modularity of the online socialsupport network and the online social discussion network Itcan be seen that the modularity Q of both is even more than08 It indicates that community structure exists widely in

Table 3 Characteristics of the whole online social network structure of athletes

NameOut-degree In-degree

Mean Std Max Min Mean Std Max MinPractical online support network 4068 3362 25000 0000 4068 1925 10000 0000Emotional online support network 2433 1880 10000 0000 2433 1537 6000 0000Social online support network 3418 3055 14000 0000 3411 1863 8000 0000Employment online discussion network 2092 2238 15000 0000 2092 1444 7000 0000Achievement online support network 2837 3384 25000 0000 2837 1869 9000 0000Revenue online discussion network 2936 2550 15000 0000 2957 1808 8000 0000Professional online discussion network 2716 2358 14000 0000 2752 1657 7000 0000Love and marriage online discussion network 2015 1728 9000 0000 2015 1468 8000 0000

Table 4 Central characteristics of the whole online social network structure of athletes

Name Eccentricity Closeness centrality Harmonic centrality Betweenness centralityPractical online support network 8247 0294 0368 251397Emotional online support network 4376 0435 0502 57780Social online support network 5266 0366 0440 129133Employment online discussion network 3092 0436 0491 21084Achievement online support network 2823 0497 0558 17440Revenue online discussion network 3832 0450 0528 28336Professional online discussion network 3694 0453 0531 20667Love and marriage online discussion network 2718 0550 0607 15389

Complexity 7

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

Table 1 Athlete online relationship matrix

N a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 a5 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 a8 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a9 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 a10 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a12 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 a13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 a15 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 a16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 a17 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 a18 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 a19 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 a20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

(a) (b)

(c) (d)

Figure 2 Continued

4 Complexity

Network density is an important metric in the structuralform of a network and is defined as the ratio of the numberof edges actually present in the network to the maximumnumber of edges that can be accommodated Networkdensity is commonly used in online social networks tomeasure the density of social relationships with higherdensity indicating more connections and the greater effec-tiveness of the networkrsquos influence on nodes +e networkdistance is used to describe the length of the shortest pathbetween nodes and the clustering coefficient reflects thedegree of network aggregation +e combination of networkdistance and clustering coefficient can demonstrate theldquosmall worldrdquo effect showing how nodes are embedded intheir surrounding nodes By referring to relevant researchresults [37ndash39] an indicator is proposed here to combine thetwo as shown in (2) and the last column of Cd is obtained asin Table 2 the higher the Cd the more obvious the ldquosmallworldrdquo effect

Cdi ci1113936ici + di1113936idi( 1113857

2 (2)

Statistics on the whole network viscosity character-istics of the athletesrsquo online social networks are shown inTable 2 +e network density of each of the athletesrsquoonline social networks was in the interval [0016 0028]indicating that the network had essentially equal influ-ence on the athletes Among the online social supportnetworks emotional online support was the most lackingand their network density was only 0016 among theonline social discussion networks the athletes were moreconcerned with income issues Comparing the averagedistance of the networks revealed that athletes had thelongest chain of online practical support relationshipsand were prone to extend online practical support re-lationships +e average clustering coefficient for love andmarriage online discussions was only 03 with the

(e) (f )

(g) (h)

Figure 2 Topology of the online social network (a) Practical online support network (b) Emotional online support network (c) Socialonline support network (d) Employment online discussion network (e) Achievement online support network (f ) Revenue onlinediscussion network (g) Professional online discussion network (h) Love and marriage online discussion network

Complexity 5

sparsest network relationships +e ldquosmall worldrdquo effectof practical online support network is most evident in theCd measure

43Centrality Centrality measures the structural propertiesof social networks at a microlevel and is usually measured bythree indicators degree centrality closeness centrality andbetweenness centrality

As shown in (3) g represents the size of the network anddegree centrality CD is the most direct indicator of thecentrality of a network node it measures the total number ofdirect links between a node and other nodes +e higher thedegree centrality is the more important the node is in thenetwork in the case of directed graphs the two parametersout-degree and in-degree need to be considered

CD Ni( 1113857 1113944

g

j1xij

CDprime Ni( 1113857

CD Ni( 1113857

g minus 1 ine j

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Closeness centrality C(x) examines the extent to which anode propagates information without relying on other nodesif a node is at a short distance from all other nodes then thatpoint is at the overall centre As shown in (4) d(x y) indicatesthe distance between node x and node y

C(x) 1

1113936yd(y x) (4)

As shown in (4) betweenness centrality characterises theextent to which a node is known as a bridge to the variousothers or the extent to which it can control others σst(v)

denotes the number of shortest paths of two nodes throughpoint v and σst denotes the total number of shortest paths oftwo nodes

CB(v) 1113944sne vne t

σst(v)

σst

(5)

+e data was processed using the formulae above +echaracteristics of the whole online social network structureof the athletes in-degree and out-degree are shown in Ta-ble 3 +e maximum values show that the out-degree is

generally greater than the in-degree indicating that athletesactively seek online support and online discussionmore thanthey passively receive it +e minimum value of in-degreeand out-degree for all networks is 0 indicating that there areathletes who do not engage in online support and onlinediscussion behaviours with others in their sport team Inaddition there is more variation between individual athletessuch as the practical online support network and achieve-ment online support networks which have a maximumvalue of 25 while both have a minimum value of 0

Table 4 shows the parameter values for the whole onlinesocial network centrality characteristics of the athletesComparing the indicators of eccentricity closeness cen-trality harmonic centrality and betweenness centrality re-veals that athletes have a preference for seeking achievementsupport over other online support Online social discussionand online social support in general show a more active andactive search for support and discussion while acceptance ismore passive In terms of the propagation of online socialsupport and online social discussion relationships athleteswere more likely to extend their daily help support rela-tionships and were susceptible to the influence ofintermediaries Overall the higher closeness centrality oflove and marriage online discussion network indicates ahigher chance of connection between nodes Harmoniccentrality is usually for nonconnected networks and can beignored here Network with higher betweenness centralityindicates that more nodes in the network play a role inconnecting these groups together such as practical onlinesupport network

44 Bipartite Relationship Tripartite Relationship Bipartiterelationship is the basic unit of statistical analysis of socialnetworks For directed networks the bipartite relationshipbetween two nodes in the network includes reciprocal re-lationships one-way relationships and nulls

Tripartite relationships ie relationships between threenodes are formed by combining three pairs of bipartiterelationships +e tripartite structure is the basis of socialstructure and is described by scholars such as Holland as 16isomorphic categories each represented by three or foursymbols the first number represents the number of recip-rocal tripartite relations the second number represents thenumber of asymmetrical tripartite relations the thirdnumber represents the number of nulls in tripartite

Table 2 +e viscosity characteristics of online social network

Name of network Density Mean distance Average clustering coefficientPractical online support network 0028 5663 0401Emotional online support network 0017 4025 0310Social online support network 0024 4672 0361Employment online discussion network 0016 3138 0314Achievement online support network 002 2781 0379Revenue online discussion network 0021 3059 0388Professional online discussion network 0019 2911 0388Love and marriage online discussion network 0016 2967 03

6 Complexity

relations and if there is a final letter it is used to distinguishbetween two similar tripartite relations (T for transmissionC for circular U for up and D for down)

+e overall number of relationships between the 147nodes in this study totalled 3668 and Tables 5 and 6 showthe proportion of each relationship to the overall relation-ship in the bipartite and tripartite relationships respectivelyIt can be seen that the athlete group has an absolute majorityproportion of the nulls in all 8 networks +e proportion ofone-way relationships is very small while the proportion ofreciprocal relationships is even smaller +is suggests thatonline one-way communication between groups of athletesis rare and two-way interaction is more difficult Examiningthe actual situation based on the training patterns of theathletes this is not unrelated to the regulation of commu-nication tools A comparison of the bipartite relationshipdata reveals that athletes interact with each other mainlythrough social online support network to enhance com-munication with each other but less in terms of marriageand emotions which may be that athletes are close to eachother before they engage in emotional confessions anddiscussions on topics such as marriage

+e very large percentage of 003 in the athletesrsquo tripartiterelationships suggests that in most cases there are no onlinesupport and online discussion relationships between two outof three people in the athletesrsquo group 012 had the secondhighest proportion indicating that a larger proportion of theonline relationships among the three athletes of which onlytwo had relationships with each other were difficult totransmit among the three and that it was difficult to com-municate and collide their perceptions effectively 300 and030C had the smallest proportion of both indicating that a

small proportion of the three athletes had one-way trans-mission relationships and two-way transmission relation-ships ie the whole online social network of athletes has apoor sense of identity and belonging in the group Bipartiterelationships are the simplest relationships to consider andtripartite relationships have complex social relationshipattributes and so are generally of greater concern

45 Community Structure Realistic social networks areoften not evenly distributed but consist of many subnet-works with high similarity of nodes within the subnetworkand low similarity of nodes outside the subnetworkresulting in a community structure +e modularity Q isused to quantify or judge the merit of community division ina network as shown in (6) It is defined as the ratio of thetotal number of edges within the community to the totalnumber of edges in the network minus an expectation valuethat is the magnitude of the ratio of the total number of edgeswithin the community to the total number of edges in thenetwork that would result from the same community as-signment if the network was set as a random network If Q isgreater than 03 then the network has a significant com-munity structure [40]

Q 1113944i

eii minus a2i1113872 1113873 1113944

i

eii minus 1113944i

a2i Tre minus e

2 (6)

Figure 3 shows the modularity of the online socialsupport network and the online social discussion network Itcan be seen that the modularity Q of both is even more than08 It indicates that community structure exists widely in

Table 3 Characteristics of the whole online social network structure of athletes

NameOut-degree In-degree

Mean Std Max Min Mean Std Max MinPractical online support network 4068 3362 25000 0000 4068 1925 10000 0000Emotional online support network 2433 1880 10000 0000 2433 1537 6000 0000Social online support network 3418 3055 14000 0000 3411 1863 8000 0000Employment online discussion network 2092 2238 15000 0000 2092 1444 7000 0000Achievement online support network 2837 3384 25000 0000 2837 1869 9000 0000Revenue online discussion network 2936 2550 15000 0000 2957 1808 8000 0000Professional online discussion network 2716 2358 14000 0000 2752 1657 7000 0000Love and marriage online discussion network 2015 1728 9000 0000 2015 1468 8000 0000

Table 4 Central characteristics of the whole online social network structure of athletes

Name Eccentricity Closeness centrality Harmonic centrality Betweenness centralityPractical online support network 8247 0294 0368 251397Emotional online support network 4376 0435 0502 57780Social online support network 5266 0366 0440 129133Employment online discussion network 3092 0436 0491 21084Achievement online support network 2823 0497 0558 17440Revenue online discussion network 3832 0450 0528 28336Professional online discussion network 3694 0453 0531 20667Love and marriage online discussion network 2718 0550 0607 15389

Complexity 7

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

Network density is an important metric in the structuralform of a network and is defined as the ratio of the numberof edges actually present in the network to the maximumnumber of edges that can be accommodated Networkdensity is commonly used in online social networks tomeasure the density of social relationships with higherdensity indicating more connections and the greater effec-tiveness of the networkrsquos influence on nodes +e networkdistance is used to describe the length of the shortest pathbetween nodes and the clustering coefficient reflects thedegree of network aggregation +e combination of networkdistance and clustering coefficient can demonstrate theldquosmall worldrdquo effect showing how nodes are embedded intheir surrounding nodes By referring to relevant researchresults [37ndash39] an indicator is proposed here to combine thetwo as shown in (2) and the last column of Cd is obtained asin Table 2 the higher the Cd the more obvious the ldquosmallworldrdquo effect

Cdi ci1113936ici + di1113936idi( 1113857

2 (2)

Statistics on the whole network viscosity character-istics of the athletesrsquo online social networks are shown inTable 2 +e network density of each of the athletesrsquoonline social networks was in the interval [0016 0028]indicating that the network had essentially equal influ-ence on the athletes Among the online social supportnetworks emotional online support was the most lackingand their network density was only 0016 among theonline social discussion networks the athletes were moreconcerned with income issues Comparing the averagedistance of the networks revealed that athletes had thelongest chain of online practical support relationshipsand were prone to extend online practical support re-lationships +e average clustering coefficient for love andmarriage online discussions was only 03 with the

(e) (f )

(g) (h)

Figure 2 Topology of the online social network (a) Practical online support network (b) Emotional online support network (c) Socialonline support network (d) Employment online discussion network (e) Achievement online support network (f ) Revenue onlinediscussion network (g) Professional online discussion network (h) Love and marriage online discussion network

Complexity 5

sparsest network relationships +e ldquosmall worldrdquo effectof practical online support network is most evident in theCd measure

43Centrality Centrality measures the structural propertiesof social networks at a microlevel and is usually measured bythree indicators degree centrality closeness centrality andbetweenness centrality

As shown in (3) g represents the size of the network anddegree centrality CD is the most direct indicator of thecentrality of a network node it measures the total number ofdirect links between a node and other nodes +e higher thedegree centrality is the more important the node is in thenetwork in the case of directed graphs the two parametersout-degree and in-degree need to be considered

CD Ni( 1113857 1113944

g

j1xij

CDprime Ni( 1113857

CD Ni( 1113857

g minus 1 ine j

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Closeness centrality C(x) examines the extent to which anode propagates information without relying on other nodesif a node is at a short distance from all other nodes then thatpoint is at the overall centre As shown in (4) d(x y) indicatesthe distance between node x and node y

C(x) 1

1113936yd(y x) (4)

As shown in (4) betweenness centrality characterises theextent to which a node is known as a bridge to the variousothers or the extent to which it can control others σst(v)

denotes the number of shortest paths of two nodes throughpoint v and σst denotes the total number of shortest paths oftwo nodes

CB(v) 1113944sne vne t

σst(v)

σst

(5)

+e data was processed using the formulae above +echaracteristics of the whole online social network structureof the athletes in-degree and out-degree are shown in Ta-ble 3 +e maximum values show that the out-degree is

generally greater than the in-degree indicating that athletesactively seek online support and online discussionmore thanthey passively receive it +e minimum value of in-degreeand out-degree for all networks is 0 indicating that there areathletes who do not engage in online support and onlinediscussion behaviours with others in their sport team Inaddition there is more variation between individual athletessuch as the practical online support network and achieve-ment online support networks which have a maximumvalue of 25 while both have a minimum value of 0

Table 4 shows the parameter values for the whole onlinesocial network centrality characteristics of the athletesComparing the indicators of eccentricity closeness cen-trality harmonic centrality and betweenness centrality re-veals that athletes have a preference for seeking achievementsupport over other online support Online social discussionand online social support in general show a more active andactive search for support and discussion while acceptance ismore passive In terms of the propagation of online socialsupport and online social discussion relationships athleteswere more likely to extend their daily help support rela-tionships and were susceptible to the influence ofintermediaries Overall the higher closeness centrality oflove and marriage online discussion network indicates ahigher chance of connection between nodes Harmoniccentrality is usually for nonconnected networks and can beignored here Network with higher betweenness centralityindicates that more nodes in the network play a role inconnecting these groups together such as practical onlinesupport network

44 Bipartite Relationship Tripartite Relationship Bipartiterelationship is the basic unit of statistical analysis of socialnetworks For directed networks the bipartite relationshipbetween two nodes in the network includes reciprocal re-lationships one-way relationships and nulls

Tripartite relationships ie relationships between threenodes are formed by combining three pairs of bipartiterelationships +e tripartite structure is the basis of socialstructure and is described by scholars such as Holland as 16isomorphic categories each represented by three or foursymbols the first number represents the number of recip-rocal tripartite relations the second number represents thenumber of asymmetrical tripartite relations the thirdnumber represents the number of nulls in tripartite

Table 2 +e viscosity characteristics of online social network

Name of network Density Mean distance Average clustering coefficientPractical online support network 0028 5663 0401Emotional online support network 0017 4025 0310Social online support network 0024 4672 0361Employment online discussion network 0016 3138 0314Achievement online support network 002 2781 0379Revenue online discussion network 0021 3059 0388Professional online discussion network 0019 2911 0388Love and marriage online discussion network 0016 2967 03

6 Complexity

relations and if there is a final letter it is used to distinguishbetween two similar tripartite relations (T for transmissionC for circular U for up and D for down)

+e overall number of relationships between the 147nodes in this study totalled 3668 and Tables 5 and 6 showthe proportion of each relationship to the overall relation-ship in the bipartite and tripartite relationships respectivelyIt can be seen that the athlete group has an absolute majorityproportion of the nulls in all 8 networks +e proportion ofone-way relationships is very small while the proportion ofreciprocal relationships is even smaller +is suggests thatonline one-way communication between groups of athletesis rare and two-way interaction is more difficult Examiningthe actual situation based on the training patterns of theathletes this is not unrelated to the regulation of commu-nication tools A comparison of the bipartite relationshipdata reveals that athletes interact with each other mainlythrough social online support network to enhance com-munication with each other but less in terms of marriageand emotions which may be that athletes are close to eachother before they engage in emotional confessions anddiscussions on topics such as marriage

+e very large percentage of 003 in the athletesrsquo tripartiterelationships suggests that in most cases there are no onlinesupport and online discussion relationships between two outof three people in the athletesrsquo group 012 had the secondhighest proportion indicating that a larger proportion of theonline relationships among the three athletes of which onlytwo had relationships with each other were difficult totransmit among the three and that it was difficult to com-municate and collide their perceptions effectively 300 and030C had the smallest proportion of both indicating that a

small proportion of the three athletes had one-way trans-mission relationships and two-way transmission relation-ships ie the whole online social network of athletes has apoor sense of identity and belonging in the group Bipartiterelationships are the simplest relationships to consider andtripartite relationships have complex social relationshipattributes and so are generally of greater concern

45 Community Structure Realistic social networks areoften not evenly distributed but consist of many subnet-works with high similarity of nodes within the subnetworkand low similarity of nodes outside the subnetworkresulting in a community structure +e modularity Q isused to quantify or judge the merit of community division ina network as shown in (6) It is defined as the ratio of thetotal number of edges within the community to the totalnumber of edges in the network minus an expectation valuethat is the magnitude of the ratio of the total number of edgeswithin the community to the total number of edges in thenetwork that would result from the same community as-signment if the network was set as a random network If Q isgreater than 03 then the network has a significant com-munity structure [40]

Q 1113944i

eii minus a2i1113872 1113873 1113944

i

eii minus 1113944i

a2i Tre minus e

2 (6)

Figure 3 shows the modularity of the online socialsupport network and the online social discussion network Itcan be seen that the modularity Q of both is even more than08 It indicates that community structure exists widely in

Table 3 Characteristics of the whole online social network structure of athletes

NameOut-degree In-degree

Mean Std Max Min Mean Std Max MinPractical online support network 4068 3362 25000 0000 4068 1925 10000 0000Emotional online support network 2433 1880 10000 0000 2433 1537 6000 0000Social online support network 3418 3055 14000 0000 3411 1863 8000 0000Employment online discussion network 2092 2238 15000 0000 2092 1444 7000 0000Achievement online support network 2837 3384 25000 0000 2837 1869 9000 0000Revenue online discussion network 2936 2550 15000 0000 2957 1808 8000 0000Professional online discussion network 2716 2358 14000 0000 2752 1657 7000 0000Love and marriage online discussion network 2015 1728 9000 0000 2015 1468 8000 0000

Table 4 Central characteristics of the whole online social network structure of athletes

Name Eccentricity Closeness centrality Harmonic centrality Betweenness centralityPractical online support network 8247 0294 0368 251397Emotional online support network 4376 0435 0502 57780Social online support network 5266 0366 0440 129133Employment online discussion network 3092 0436 0491 21084Achievement online support network 2823 0497 0558 17440Revenue online discussion network 3832 0450 0528 28336Professional online discussion network 3694 0453 0531 20667Love and marriage online discussion network 2718 0550 0607 15389

Complexity 7

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

sparsest network relationships +e ldquosmall worldrdquo effectof practical online support network is most evident in theCd measure

43Centrality Centrality measures the structural propertiesof social networks at a microlevel and is usually measured bythree indicators degree centrality closeness centrality andbetweenness centrality

As shown in (3) g represents the size of the network anddegree centrality CD is the most direct indicator of thecentrality of a network node it measures the total number ofdirect links between a node and other nodes +e higher thedegree centrality is the more important the node is in thenetwork in the case of directed graphs the two parametersout-degree and in-degree need to be considered

CD Ni( 1113857 1113944

g

j1xij

CDprime Ni( 1113857

CD Ni( 1113857

g minus 1 ine j

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Closeness centrality C(x) examines the extent to which anode propagates information without relying on other nodesif a node is at a short distance from all other nodes then thatpoint is at the overall centre As shown in (4) d(x y) indicatesthe distance between node x and node y

C(x) 1

1113936yd(y x) (4)

As shown in (4) betweenness centrality characterises theextent to which a node is known as a bridge to the variousothers or the extent to which it can control others σst(v)

denotes the number of shortest paths of two nodes throughpoint v and σst denotes the total number of shortest paths oftwo nodes

CB(v) 1113944sne vne t

σst(v)

σst

(5)

+e data was processed using the formulae above +echaracteristics of the whole online social network structureof the athletes in-degree and out-degree are shown in Ta-ble 3 +e maximum values show that the out-degree is

generally greater than the in-degree indicating that athletesactively seek online support and online discussionmore thanthey passively receive it +e minimum value of in-degreeand out-degree for all networks is 0 indicating that there areathletes who do not engage in online support and onlinediscussion behaviours with others in their sport team Inaddition there is more variation between individual athletessuch as the practical online support network and achieve-ment online support networks which have a maximumvalue of 25 while both have a minimum value of 0

Table 4 shows the parameter values for the whole onlinesocial network centrality characteristics of the athletesComparing the indicators of eccentricity closeness cen-trality harmonic centrality and betweenness centrality re-veals that athletes have a preference for seeking achievementsupport over other online support Online social discussionand online social support in general show a more active andactive search for support and discussion while acceptance ismore passive In terms of the propagation of online socialsupport and online social discussion relationships athleteswere more likely to extend their daily help support rela-tionships and were susceptible to the influence ofintermediaries Overall the higher closeness centrality oflove and marriage online discussion network indicates ahigher chance of connection between nodes Harmoniccentrality is usually for nonconnected networks and can beignored here Network with higher betweenness centralityindicates that more nodes in the network play a role inconnecting these groups together such as practical onlinesupport network

44 Bipartite Relationship Tripartite Relationship Bipartiterelationship is the basic unit of statistical analysis of socialnetworks For directed networks the bipartite relationshipbetween two nodes in the network includes reciprocal re-lationships one-way relationships and nulls

Tripartite relationships ie relationships between threenodes are formed by combining three pairs of bipartiterelationships +e tripartite structure is the basis of socialstructure and is described by scholars such as Holland as 16isomorphic categories each represented by three or foursymbols the first number represents the number of recip-rocal tripartite relations the second number represents thenumber of asymmetrical tripartite relations the thirdnumber represents the number of nulls in tripartite

Table 2 +e viscosity characteristics of online social network

Name of network Density Mean distance Average clustering coefficientPractical online support network 0028 5663 0401Emotional online support network 0017 4025 0310Social online support network 0024 4672 0361Employment online discussion network 0016 3138 0314Achievement online support network 002 2781 0379Revenue online discussion network 0021 3059 0388Professional online discussion network 0019 2911 0388Love and marriage online discussion network 0016 2967 03

6 Complexity

relations and if there is a final letter it is used to distinguishbetween two similar tripartite relations (T for transmissionC for circular U for up and D for down)

+e overall number of relationships between the 147nodes in this study totalled 3668 and Tables 5 and 6 showthe proportion of each relationship to the overall relation-ship in the bipartite and tripartite relationships respectivelyIt can be seen that the athlete group has an absolute majorityproportion of the nulls in all 8 networks +e proportion ofone-way relationships is very small while the proportion ofreciprocal relationships is even smaller +is suggests thatonline one-way communication between groups of athletesis rare and two-way interaction is more difficult Examiningthe actual situation based on the training patterns of theathletes this is not unrelated to the regulation of commu-nication tools A comparison of the bipartite relationshipdata reveals that athletes interact with each other mainlythrough social online support network to enhance com-munication with each other but less in terms of marriageand emotions which may be that athletes are close to eachother before they engage in emotional confessions anddiscussions on topics such as marriage

+e very large percentage of 003 in the athletesrsquo tripartiterelationships suggests that in most cases there are no onlinesupport and online discussion relationships between two outof three people in the athletesrsquo group 012 had the secondhighest proportion indicating that a larger proportion of theonline relationships among the three athletes of which onlytwo had relationships with each other were difficult totransmit among the three and that it was difficult to com-municate and collide their perceptions effectively 300 and030C had the smallest proportion of both indicating that a

small proportion of the three athletes had one-way trans-mission relationships and two-way transmission relation-ships ie the whole online social network of athletes has apoor sense of identity and belonging in the group Bipartiterelationships are the simplest relationships to consider andtripartite relationships have complex social relationshipattributes and so are generally of greater concern

45 Community Structure Realistic social networks areoften not evenly distributed but consist of many subnet-works with high similarity of nodes within the subnetworkand low similarity of nodes outside the subnetworkresulting in a community structure +e modularity Q isused to quantify or judge the merit of community division ina network as shown in (6) It is defined as the ratio of thetotal number of edges within the community to the totalnumber of edges in the network minus an expectation valuethat is the magnitude of the ratio of the total number of edgeswithin the community to the total number of edges in thenetwork that would result from the same community as-signment if the network was set as a random network If Q isgreater than 03 then the network has a significant com-munity structure [40]

Q 1113944i

eii minus a2i1113872 1113873 1113944

i

eii minus 1113944i

a2i Tre minus e

2 (6)

Figure 3 shows the modularity of the online socialsupport network and the online social discussion network Itcan be seen that the modularity Q of both is even more than08 It indicates that community structure exists widely in

Table 3 Characteristics of the whole online social network structure of athletes

NameOut-degree In-degree

Mean Std Max Min Mean Std Max MinPractical online support network 4068 3362 25000 0000 4068 1925 10000 0000Emotional online support network 2433 1880 10000 0000 2433 1537 6000 0000Social online support network 3418 3055 14000 0000 3411 1863 8000 0000Employment online discussion network 2092 2238 15000 0000 2092 1444 7000 0000Achievement online support network 2837 3384 25000 0000 2837 1869 9000 0000Revenue online discussion network 2936 2550 15000 0000 2957 1808 8000 0000Professional online discussion network 2716 2358 14000 0000 2752 1657 7000 0000Love and marriage online discussion network 2015 1728 9000 0000 2015 1468 8000 0000

Table 4 Central characteristics of the whole online social network structure of athletes

Name Eccentricity Closeness centrality Harmonic centrality Betweenness centralityPractical online support network 8247 0294 0368 251397Emotional online support network 4376 0435 0502 57780Social online support network 5266 0366 0440 129133Employment online discussion network 3092 0436 0491 21084Achievement online support network 2823 0497 0558 17440Revenue online discussion network 3832 0450 0528 28336Professional online discussion network 3694 0453 0531 20667Love and marriage online discussion network 2718 0550 0607 15389

Complexity 7

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

relations and if there is a final letter it is used to distinguishbetween two similar tripartite relations (T for transmissionC for circular U for up and D for down)

+e overall number of relationships between the 147nodes in this study totalled 3668 and Tables 5 and 6 showthe proportion of each relationship to the overall relation-ship in the bipartite and tripartite relationships respectivelyIt can be seen that the athlete group has an absolute majorityproportion of the nulls in all 8 networks +e proportion ofone-way relationships is very small while the proportion ofreciprocal relationships is even smaller +is suggests thatonline one-way communication between groups of athletesis rare and two-way interaction is more difficult Examiningthe actual situation based on the training patterns of theathletes this is not unrelated to the regulation of commu-nication tools A comparison of the bipartite relationshipdata reveals that athletes interact with each other mainlythrough social online support network to enhance com-munication with each other but less in terms of marriageand emotions which may be that athletes are close to eachother before they engage in emotional confessions anddiscussions on topics such as marriage

+e very large percentage of 003 in the athletesrsquo tripartiterelationships suggests that in most cases there are no onlinesupport and online discussion relationships between two outof three people in the athletesrsquo group 012 had the secondhighest proportion indicating that a larger proportion of theonline relationships among the three athletes of which onlytwo had relationships with each other were difficult totransmit among the three and that it was difficult to com-municate and collide their perceptions effectively 300 and030C had the smallest proportion of both indicating that a

small proportion of the three athletes had one-way trans-mission relationships and two-way transmission relation-ships ie the whole online social network of athletes has apoor sense of identity and belonging in the group Bipartiterelationships are the simplest relationships to consider andtripartite relationships have complex social relationshipattributes and so are generally of greater concern

45 Community Structure Realistic social networks areoften not evenly distributed but consist of many subnet-works with high similarity of nodes within the subnetworkand low similarity of nodes outside the subnetworkresulting in a community structure +e modularity Q isused to quantify or judge the merit of community division ina network as shown in (6) It is defined as the ratio of thetotal number of edges within the community to the totalnumber of edges in the network minus an expectation valuethat is the magnitude of the ratio of the total number of edgeswithin the community to the total number of edges in thenetwork that would result from the same community as-signment if the network was set as a random network If Q isgreater than 03 then the network has a significant com-munity structure [40]

Q 1113944i

eii minus a2i1113872 1113873 1113944

i

eii minus 1113944i

a2i Tre minus e

2 (6)

Figure 3 shows the modularity of the online socialsupport network and the online social discussion network Itcan be seen that the modularity Q of both is even more than08 It indicates that community structure exists widely in

Table 3 Characteristics of the whole online social network structure of athletes

NameOut-degree In-degree

Mean Std Max Min Mean Std Max MinPractical online support network 4068 3362 25000 0000 4068 1925 10000 0000Emotional online support network 2433 1880 10000 0000 2433 1537 6000 0000Social online support network 3418 3055 14000 0000 3411 1863 8000 0000Employment online discussion network 2092 2238 15000 0000 2092 1444 7000 0000Achievement online support network 2837 3384 25000 0000 2837 1869 9000 0000Revenue online discussion network 2936 2550 15000 0000 2957 1808 8000 0000Professional online discussion network 2716 2358 14000 0000 2752 1657 7000 0000Love and marriage online discussion network 2015 1728 9000 0000 2015 1468 8000 0000

Table 4 Central characteristics of the whole online social network structure of athletes

Name Eccentricity Closeness centrality Harmonic centrality Betweenness centralityPractical online support network 8247 0294 0368 251397Emotional online support network 4376 0435 0502 57780Social online support network 5266 0366 0440 129133Employment online discussion network 3092 0436 0491 21084Achievement online support network 2823 0497 0558 17440Revenue online discussion network 3832 0450 0528 28336Professional online discussion network 3694 0453 0531 20667Love and marriage online discussion network 2718 0550 0607 15389

Complexity 7

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

Table 6 Distribution of tripartite relationship

Type

Practicalonlinesupportnetwork

Emotionalonlinesupportnetwork

Socialonlinesupportnetwork

Employmentonline discussion

network

Achievementonline support

network

Revenueonline

discussionnetwork

Professionalonline

discussionnetwork

Loveand marriage

onlinediscussionnetwork

003 735 9132 8474 8904 8679 9524 8784 9262012 1647 705 1066 972 1094 406 967 602102 772 139 389 067 158 063 187 112021D 041 005 014 020 023 002 017 008021U 027 006 010 017 011 001 019 006021C 036 007 014 010 015 002 010 005111D 032 002 013 002 003 001 003 004111U 040 001 009 003 008 001 005 000030T 010 001 003 004 004 000 003 000030C 001 000 000 000 000 000 000 001201 012 001 003 000 001 000 002 000120D 008 000 002 000 001 000 001 000120U 006 000 001 000 002 000 001 000120C 005 000 001 000 000 000 000 000210 010 000 001 000 001 000 001 000300 003 000 001 000 000 000 000 000

13

Size distribution2422201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12Modularity class

Modularity 0854Modularity with resolution 0854Number of communities 13

(a)

Size distribution201816141210

86420

Size

(num

ber o

f nod

es)

ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13Modularity class

14 15 16 17

Modularity 0867Modularity with resolution 0867Number of communities 19

(b)

Figure 3 Modularization of community structure (a) Modularity for online social support network (b) Modularity for online socialdiscussion network

Table 5 Distribution of bipartite relationship

Name Reciprocal relationships () One-way relationship () Nothingness ()Practical online support network 305 669 9026Emotional online support network 049 249 9702Social online support network 142 393 9465Employment online discussion network 024 361 9614Achievement online support network 059 408 9534Revenue online discussion network 022 139 9839Professional online discussion network 051 406 9543Love and marriage online discussion network 033 331 9636

8 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

athletesrsquo online social networks A relatively stable com-munity structure is very important for the physical andmental development of athletes

5 Conclusion

In summary the network density of the athletesrsquo onlinesocial support network is greater than that of the onlinesocial discussion network and specifically among the sub-networks the practical online support network is the mostdense and the love and marriage online discussion networkis the least dense +is indicates that in recent years pro-fessional athletes have been gradually increasing their onlinepractical support claims in the course of their daily lives andtraining Athletes also show higher social online supportindicating that in the new era and environment newathletes still attach more importance to social interactionand they are actively expanding their life circle

+e proportion of the relational composition of athletesrsquoonline social support networks has also changed in a moreinteresting way While the proportion of teammates and familymembers remains high overall some studies have shown thatthe proportion of social support provided by family membershas declined significantly while the social support provided byclassmates or friends even surpasses that of family members[27] a feature that is particularly evident when it comes to socialonline support Of course it is still important not to overlookthe strong social support power of teammates which is un-matched by any other social role

In terms of strong and weak relationships athletesrsquoonline social support networks still show a strong tendencytowards ldquostrong relationshipsrdquo but compared to onlinesocial discussion networks weak relationships are slowlygaining ground especially in social online support wherethe proportion of weak relationships reaches almost 40+is is mainly due to the fact that classmates or friends play agreater role in this area while teammanagers have the lowestpercentage which is also related to the authority of themanagers and the fact that athletes are more distant fromcoaches and instructors and have to turn to their teammatesor classmates for social support

Data Availability

+e original data used in this study are the questionnairedata obtained from the survey +e original data used tosupport the findings of this study are available from thecorresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported in part by the National NaturalScience Foundation of China under Grant nos 61440036and 61040029 and the National Social Science Foundation ofChina under Grant no 16ATY002

References

[1] J Ding and H Qian ldquoA study on the multi-level relationshipbetween the overall social network of Chinese professionalathletesrdquo in Proceedings of the 2015 Abstract of papers of theTenth National Sports Science Congress pp 1217-1218 ChinaSports Science Society Hangzhou Jiangsu January 2015

[2] H Qian and X Zhang ldquoEffects of personal characteristics ofChinese professional athletes on the structure of social sup-port networkrdquo Journal of Shanghai Institute of Physical Ed-ucation vol 38 no 6 pp 59ndash63 2014

[3] H Qian X Yang J Ding et al ldquoAnalysis of social networkcharacteristics of Chinese professional athletesrdquo Journal ofWuhan Institute of Physical Education vol 50 no 7pp 77ndash83 2016

[4] H Qian and J Ding ldquoAnalysis of the overall social networkcharacteristics of Chinese professional athletesrdquo in Proceed-ings of the Compendium of Abstracts of the 10th NationalSports Science Conference 2015 pp 811ndash813 Chinese Societyof Sports Science Hangzhou Jiangsu September 2015

[5] X Zhang and H Qian ldquoResearch on structural characteristicsof job search network of Chinese professional athletesmdashbasedon sample survey of professional athletes in Shaanxi prov-incerdquo Journal of Wuhan Institute of Physical Educationvol 52 no 3 pp 17ndash23 2018

[6] Z Xiong A Study on Community Discovery Technology and itsApplication in Online Social Network Central South Uni-versity Changsha China 2012

[7] C Xiao Analysis and Prediction of Userrsquos Behavior in OnlineSocial Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[8] Z Li A Study on the Measurement and Law of InformationDissemination of Node Information in Social Network HarbinInstitute of Technology Harbin China 2015

[9] Y Su A Study on the Communication Model and Interventionof Public Opinion in Online Social Network Yanshan Uni-versity Qinhuangdao China 2018

[10] L Wang and X Cheng ldquoDynamic community discovery andevolution of online social networkrdquo Journal of ComputerScience vol 38 no 2 pp 219ndash237 2014

[11] Y Chen Z Li X Liang et al ldquoA review of online socialnetwork rumor detectionrdquo Chinese Journal of Computersvol 41 no 7 pp 1648ndash1677 2017

[12] Li Qian B Liu and Y Zhao ldquoConstruction of statisticalmetadata in the big data environmentrdquo Statistics and Infor-mation Forum vol 35 no 03 pp 14ndash20 2020

[13] R Zhang L-X Liu X-B Tang and B-R Zhang ldquoResearchon the prediction of commodity retail price index based onweb search data in the context of big datardquo Statistics andInformation Forum vol 35 no 11 pp 49ndash56 2020

[14] Z Pang and M Zeng ldquoHas internet use affected youthsubjective well-being -an analysis of CGSS data from2010ndash2015rdquo Journal of Xirsquoan University of Finance and Eco-nomics vol 33 no 03 pp 71ndash77 2020

[15] H Li and Y Chen ldquoResearch on the generation and dis-semination mechanism of network public opinionmdashbased onthe perspective of big data social network analysisrdquo Age ofMedia Contemporary Communications vol 186 no 1pp 24-25 2016

[16] X Wang ldquoData science and social networks big data smallworldrdquo Science and Society vol 1 no 1 pp 27ndash35 2014

[17] M Jia H Xu J Wang et al Handling Big Data of OnlineSocial Networks on a Small Machine Springer InternationalPublishing New York NY USA 2015

Complexity 9

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity

[18] Y Tian Y Lin and L Gong ldquoResearch on the influence ofInternet culture on campus culture in the Internet era--analysisbased on questionnaire survey of teachers and students in someuniversities in Shaanxirdquo Statistics and Information Forumvol 35 no 07 pp 122ndash128 2020

[19] J Ding L Xu H Qian et al ldquoA study on the multi-levelrelationship of the overall social network of Chinese pro-fessional athletesrdquo Journal of Xirsquoan Institute of Physical Ed-ucation Nol vol 4 pp 405ndash409 2016

[20] J Ding and H Qian ldquoA central analysis of the overall socialnetwork of professional athletes in Chinardquo A Journal of XirsquoanUniversity of Technology vol 36 no 5 pp 408ndash413 2016

[21] Y Qian Online Social Networking Analysis Electronic In-dustry Press Beijing China 2014

[22] Y Zhao and J Luo ldquoHow tomeasure social capital a review ofempirical researchrdquo Social Sciences Abroad no 2 pp 18ndash242005

[23] X Jin Y Ren and H du Change of Social Network andConceptual Behavior of Migrant Workers Social SciencesPress Beijing China 2014

[24] J S A W Carolyn ldquoAP primer logit models for socialnetworksrdquo Social Networks vol 21 no 1 pp 37ndash66 1999

[25] Z Li and J Luo ldquoA view on local management theory fromthe perspective of social networkrdquo Journal of Managementvol 8 no 12 pp 1737ndash1747 2011

[26] Z Li and J Luo ldquo+e social behavior and relational networkcharacteristics of Chinesemdashviewpoint of a social networkrdquoSocial Science Front vol 199 no 1 pp 159ndash164 2012

[27] J Luo and F Zeng ldquoA study on organization based oncomplex system perspectiverdquo Foreign Economics and Man-agement vol 41 no 12 pp 112ndash134 2019

[28] J Liu ldquoPractical Guide to Integrated Network Analysis UCI-NET Software GE Zhi Publishing House rdquo Shanghai China2014

[29] K Xu S Zhang H Chen et al ldquoMeasurement and analysis ofonline social networkrdquo Chinese Journal of Computer vol 37no 1 pp 165ndash188 2014

[30] Y Ren S Li H Du et al ldquoAn analysis of the social networkstructure of migrant workersrdquo A Journal of Xirsquoan JiaotongUniversity (Social Sciences Edition) vol 91 no 5 pp 44ndash512008

[31] Q Huang S F Fung B Liu et al ldquoModeling for professionalathletesrsquo social networks based on statistical machine learn-ingrdquo Advanced Data Mining Methods for Social Computingvol 8 2019

[32] J Liu ldquoA study on social network modelrdquo Sociological Studiesvol 1 pp 1ndash12 2004

[33] J Liu A Study on Social Network Extraction Technology forText-Oriented Information and its Application University ofDefence Science and Technology Changsha China 2009

[34] Y Wang Field T Li et al ldquoVisual analysis of shipping re-cruitment information based on Gephirdquo Big Data vol 4no 3 pp 81ndash91 2018

[35] S Hussain L Muhammad and Y Atomsa ldquoMining socialmedia and DBpedia data using Gephi and Rrdquo Journal ofApplied Computer Science amp Mathematics vol 12 no 25pp 14ndash20 2018

[36] Y Guan Y Xiang and C Kang ldquoResearch and application ofvisual analysis method based on Gephirdquo TelecommunicationsScience vol 29 no S1 pp 112ndash119 2013

[37] F Xiong X Wang S Pan H Yang H Wang and C ZhangldquoSocial recommendation with evolutionary opinion dynam-icsrdquo IEEE Transactions on Systems Man and CyberneticsSystems vol 50 no 10 pp 3804ndash3816 2020

[38] Y Hu F Xiong S Pan X Xiong L Wang and H ChenldquoBayesian personalized ranking based on multiple-layerneighborhoodsrdquo Information Sciences vol 542 pp 156ndash1762021

[39] F Xiong W Shen H Chen S Pan X Wang and Z YanldquoExploiting implicit influence from information propagationfor social recommendationrdquo IEEE Transactions on Cyber-netics vol 50 no 10 pp 4186ndash4199 2020

[40] S L Deng B Wang B Wu et al ldquoModeling and validation ofcomplex network association partitioning based on infor-mation entropyrdquo Computer Research and Developmentvol 49 no 4 pp 725ndash734 2012

10 Complexity