analyzing the maritime transportation system in greece: a

Analyzing the Maritime Transportation Systemin Greece: a Complex Network Approach

Dimitrios Tsiotas & Serafeim Polyzos

Published online: 25 November 2014# Springer Science+Business Media New York 2014

Abstract Maritime networks of coastal and insular countries constitute fundamentaltransportation systems affecting the economy and the developmental dynamics of theircountries. Under this perspective, the present article studies the Greek Maritimetransportation Network (GMN), by using a complex network approach for the part ofstructural analysis and empirical techniques for the socioeconomic evaluation of theGMN’s topology. A methodological framework is developed for dealing with theGMN’s disconnectivity, which is evaluated by the empirical analysis. The curve fittingprocedure on the degree distribution data indicated the existence of some scale-freenetwork properties of the GMN, which seemed to be also captured as high correlationsbetween pairs of binary and their homologous distance-weighted node structuralvariables, electing a topic of further empirical research on various networks. Thisstatus implies a kind of GMN’s structural indifference to distance, favoring thedevelopment of transportation activities into greater distances within the GMN. Also,the linear regression analysis modeled the connectivity of the GMN, electing topolog-ical, spatial and socioeconomic information. Finally, this paper elected the utility ofcomplex network analysis in the study of national maritime networks, capable inproviding new insights to the transportation policy makers of Greece.

Keywords Complex network analysis . Methodological framework .Maritimenetworks . Regional science . Network theory

1 Introduction

Maritime networks may be classified among the oldest forms of spatial communicationand their architecture can be surely considered that it affected and still affects the further

Netw Spat Econ (2015) 15:981–1010DOI 10.1007/s11067-014-9278-y

D. Tsiotas (*) : S. PolyzosDepartment of Planning and Regional Development, University of Thessaly, Pedion Areos, Volos 38 334,Greecee-mail: [email protected]

S. Polyzose-mail: [email protected]

procedure of the worldwide economic evolution (Ducruet and Beauguitte 2013). Thisindicates that the study of the maritime communication systems and the understandingof their structure, geography, operational mechanisms and evolutionary patterns(Ducruet and Notteboom 2012) suggest a considerable effort for the stakeholders andpolicy makers of the worldwide economic system. In the recent years, the complexity ofmodern economies’ spatial and industrial organization favor a multi-actor and multi-modal pattern configuration (Zwier et al. 1995), leading to the establishment ofNetworkTheory (Borgatti and Halgin 2011; Wang et al. 2011; Tsiotas and Polyzos 2013a;Caschili et al. 2014) and particularly Complex Network Analysis (Albert and Barabasi2002; Schintler et al. 2007; Ducruet and Beauguitte 2013) as a separate scientific sectorthat constitutes a fundamental tool of geography and spatial analysis, providing a newframework of analytical techniques and methods for spatial economic analysis.

In this modern analytical framework, maritime networks employ a fundamentalportion of complex network analysis, since they represent spatial communicationsystems producing voluminous flows of socio-economic interest, such as tourism andtrade flows. In terms of trade, an amount of about 90 % of the worldwide trade istransported by sea, fact that it is economically interpreted to a 70 % of the worldwidetrade value (Windeck 2013). On the other hand, maritime networks also providefundamental transportation services to tourism, where large tourist masses reachannually their coastal and insular tourism destinations. Even more, the mean ofmaritime transportation suggests a tourism resource by itself, constituting a market thatis estimated to possess almost the 10 % (Diakomihalis 2007) of the total expenditure ofthe worldwide tourism.

Under the above perspective, this article studies the Greek Maritime Network(GMN), by using measures of complex network analysis and empirical techniques,taking under consideration that the maritime activity in Greece is listed as one of themost important components of its economy. In numeral terms, the Greek maritimepassenger system constitutes a transportation system having annual carrying capacityestimated to 55 million passengers, fact that sets Greece into the first place (possessingthe highest share of about 30 %) in the list of European maritime transportation and intoone of the highest places in the respective world ranking (Tzannatos 2005).

Utilizing complex network analysis for modeling spatial networks generally benefitsa macroscopic spatial and socioeconomic approach for these physical communicationsystems (Ducruet and Beauguitte 2013). This article applies for the first time, accordingto the best of our knowledge, this analytical tool for studying maritime transportationsystems at national level and surely this stands for the case of Greece. Works of similarthematic framework conducted until now (Fremont 2007; Hu and Zhu 2009; Ducruetet al. 2010) apply complex network analysis on maritime transportation systems oflarger geographic scale, such as global, intercontinental or international, and othersthat are applicable in the similar geographic scale (Wang et al. 2011; Lin 2012) studyother means of transportation, such as aviation networks.

The study of maritime transportation systems in national scale is driven by differentcharacteristics than the respective international and global scale studies, fact thatrenders a different perspective to this article. The first difference is due to scale. Ininternational and global maritime networks, the distances, the size of ports and thevolume of flows are greater than these of national maritime networks, inducingeconomies of scale (Tang et al. 2011) that are not present in the majority of the national

982 D. Tsiotas, S. Polyzos

cases. This gives to the ports of global maritime networks the opportunity to evolvesometimes faster than the growth rates of their countries, affecting secondarily thehinterland’s development, depending on their position in the global network and theincentives policy that they adopt (shipping margins, infrastructure investments, etc.)(Marquez-Ramos et al. 2011).

In opposition, the evolution of national maritime networks seems to be more endog-enously ruled, depending basically on the developmental dynamics of each country. Inreality, there is an interactive relation between the developmental dynamics of a countryand its transportation system (Blumenfeld-Lieberthal 2008; Xie and Levinson 2009; Szetoet al. 2013). In particular, every endogenous alternation in a transportation network (suchas the connection of a new place) induces microeconomic effects that through a complexmechanism affect the national and regional economy (Xie and Levinson 2009) and, viceversa, an amount of macroeconomic factors, such as transportation and economic policies,affect the structure of the national transportation networks (Blumenfeld-Lieberthal 2008).Additionally, the topology of transportation networks can be used as an index of theeconomic development of a country.Within this framework, the study of the topology of anational maritime transportation network obviously provides better insights for theeconomic identity of a country than the study of an international maritime system thatthat represents a polysynthetic economic pattern.

Next, the global maritime networks seem to “lack of tantamount competitors”,implying that such enormous networks are developed to serve needs that, in themajority of cases, they cannot be served or they are partially being served by othercompetitive transportation modes, due to the higher cost of conducting distant hinter-land transportations (Notteboom 2004). This observation illustrates the high connec-tivity of such global, international and intercontinental maritime networks, in opposi-tion to the national cases, where the existence of competitive modes of transportationmay produce disconnected national networks, consisting of separate components.

Also, according to the literature (Notteboom 2004; Fremont 2007; Ducruet andNotteboom 2012; Windeck 2013), it is obvious that the global and intercontinentalmaritime networks, with the exemption of the international and intercontinental cruisesthat suggest a particular aspect of tourism, mainly refer to supply network chains that theyare specializing to cargo transport and they are producing commodity network flows.This statement implies that the global and the intercontinental maritime networks are morecohesive than the domestic networks and thus they are more resistant to seasonality effectsor disease spreading, which mainly describe the passenger transport networks.

Within this framework, the study of the maritime transport system in Greece is ruled byboth the aforementioned characteristics and by a set of extra peculiarities. The firstcharacteristic is evident from the Greek history and concerns the geostrategic importanceof the geographical position of the country in the map. Greece is a country that is locatedbetween two continents (Europe and Asia) and among three seas (Black Sea, Aegean andthe Mediterranean), setting by default its national maritime transportation system as apoint of economic and political interest. The second characteristic concerns the impor-tance that the maritime activity (Tzannatos 2005) and the tourism activity (Polyzos et al.2013a) have in the Greek economy, which are obviously spatial dependent.

Additionally, the complex insular morphology of Greece (Tzannatos 2005), having alarge number of islands, suggests an important motivation for studying its maritimesystem. According to the Greek National Census (ELSTAT 2011), the Greek islands,

Analyzing the Maritime Transportation System in Greece 983

islets and rocky islands that are recorded in the regional sub-directories exceed thenumber of 1’350, from which over 230 are inhabited. This, in conjunction with the factthat Greece is a small country that it is placed within an area of 132 thousand squarekilometers (m2), illustrates the obvious insular ontology of Greece, implying itssignificant maritime activity.

Another peculiarity of the GMN is the intense seasonality in tourism activitybetween the summer period and the remainder of the year, which it is even differen-tiated within the summer period itself. It is remarkable that the population of the islandregions, excluding Crete, exceeds at the summer period the amount of 6 million people,including permanent residents and visitors, when at the remainder period of the year itis less than 1 million (Polyzos et al. 2013a). Obviously, such demographic seasonalityinduces serious consequences to the operational efficiency and consequently to thetopology of the network, influencing the total transportation capability of the country.

The final peculiarity is that the GMN is a disconnected network, consisting of separateconnected components. This is, primarily, due to scale, as it was previously noted, whichallows the development of competitive transportation modes (coastal road transportationand insular air-transport) and, further, due to the complex coastal and insular morphologyof Greece that favors the development of multi-mode transportation services.

Despite the fact that, in the topological space, the GMN constitutes a disconnectednetwork, where the distance between a pair of disconnected nodes is defined as infinite(Koschutzki et al. 2005), in the physical space this maritime system is a spatial networkthat represents an aspect of the Greek socioeconomic system. This consideration allowsinterpreting the GMN as a spatio-economic unity that was diachronically ruled by aconsistent set of developmental norms, setting a conceptual link among the discon-nected GMN’s components, which allows making conventions in order to define aglobal GMN’s topology aiming to the application of spatial analysis.

In general, the research orientation of this article is ruled by the rationale that,diachronically, the spatial communication systems reflect on their architecture and ontheir topology some information about the society that utilizes these systems and itscultural and cognitive attributes. Within this framework, the main research hypothesis ofthis paper is whether the GMN embodies, inside its topology, information of the economicand particular of the tourism dynamics of Greece and in what level such thing is done.Also, this paper proposes an empirical technique for detecting how distance affects anetwork’s structure, suggesting a further topic of empirical research on various networks.

Consequently, testing the applicability and the effectiveness of this modern model-ing network approach in Greece becomes a more interesting treatment today, sinceGreece is currently being subjected to an unconventional model of economic crisis,which for many analysts depict structural deficiencies of the European or even theglobal banking system (Polyzos et al. 2013b). Greece needs more than ever today toutilize both the common and the untried available research methods, in order to acquirea more in-depth knowledge for its developmental dynamics that will reignite thedevelopmental dynamics of the country.

The remainder of this article is organized as follows: Section 2 presents themethodology; the Graph Theoretical modeling of the GMN, the available data, thequantitative and statistical tools and the methodological framework of the analysis.Section 3 illustrates the results of the analysis and their interpretation and finally, atSection 4 conclusions are given.


2 Methodology and Data

2.1 Topological Grouping

The GMN is modeled by a disconnected, non-directed, distance-weighted graph G(V,E)(Fig. 1a) (Diestel 2005; Tsiotas et al. 2012), consisting of a set of 87 components(subgraphs) Gi(Vi,Ei)⊂G(V,E), i=1,…,87, as it is presented in the Force Atlas (Bastianet al. 2009) layout (Fig. 1b). Among these components, 77 represent isolated nodesGi({v}i⊂V(G),Ø) and 5 dipoles Gi({v,u}i⊂V(G),{e}j⊂E(G)). The first large 112-nodecomponent, comp#1≡G1(|V1|=112,|E1|=194), is located at the Aegean Sea, namedAegean component, while the second distinct 18-node component, comp#2≡G2(|V2|=18,|E2|=21), is located at the Ionian Sea, named Ionian component. Further, amongthese components we can count 3 thinner components comp#3≡G3(|V3|=3,|E3|=3),comp#4≡G4(|V4|=4,|E4|=4) and comp#5≡G5(|V5|=5,|E5|=4).

Evaluating this topological grouping in terms of spatial analysis seems improper,since it shrinks the size of the two large (Aegean and Ionian) components, consideringthem spatially equivalent with an isolated node. In order to apply a more proper spatialanalytic grouping, the 87 topological components are grouped into 7 components, bymerging the isolated nodes and the dipoles into one group per case.

In particular, the group of the 77 isolated nodes is merged into one component(comp#7), being subdivided into 4 geographical (constituting three thematic) clusters,the Aegean (comp#7a), the Ionian (comp#7b), the Cretan (comp#7c) and theHinterland (comp#7d) cluster, as it is shown in Fig. 2a. The isolated nodes of theAegean and the Ionian GMN’s clusters are not connected, due to the existence ofneighbor competitive ports of higher importance. This status refers to the existence ofcompetition “within” the same transportation mode. The isolated nodes of theHinterland are not connected to the GMN, due to the existence of competition“between” different transportation modes, implying that the existence of road or railconnections to these ports obstruct the further development of maritime connections.The state of Crete is hybrid and thus it is considered as an individual cluster. Theisolated nodes of the northern Crete are unconnected due to the existence of

Fig. 1 The graph theoretical model of the Greek Maritime Network (GMN), presented in a L-spacerepresentation and b Force Atlas (Bastian et al. 2009) layouts


competition within the transportation mode, while these of southern Crete due to theexistence of competition between different transportation modes.

On the other hand, the bipolar components are merged into a single component, thebipolar component (comp#6). In accordance to the previous rationale, two patterns ofbipolar performance are recognized, producing a pair of bipolar clusters. The first(comp#6a) refers to the dipoles that mainly serve transit needs, connecting largehinterland areas. This is the dipole Rio–Antirio that connects the Central Greece toPeloponnese and the dipole Eretreia Euvoias–Oropos that connects the Central Greeceto Euvoia. The second bipolar cluster (comp#6b) includes dipoles that serve connec-tivity needs into regions that otherwise, without the existence of the bipolar connection,they would be isolated. In this category one port of the dipole has a well establishedtransportation connection to the hinterland or to the region’s core, serving connectivityneeds with the second port. Cases that are included in this category are the dipolesPisaetos (island of Ithaka) – Sami (prefecture of Kefallonia), Megara (prefecture ofAttiki) – Faneromeni (island of Salaminas) and Astakos (Aitoloakarnania prefecture) –Metikas (island of Ithaka).

2.2 Graph Theoretical Modeling and Data

The L-space representation (Barthelemy 2011) is chosen for constructing the GMN(Fig. 1), where nodes are connected if they constitute consecutive stops on a givenroute. Intuitively, the L-space representation resembles to the physical representation,under the only difference that the edges in the L-space are drawn as linear segments,while in the physical representation they retain their real shape, being drawn as curves.The L-space representation is considered better than the physical representation, be-cause it has less cost of graphical modeling and illustration, preserving simultaneouslythe topological and spatial structure of the physical (real) maritime network.

In comparison to the P-space representation, also called “space of changes”, where apair of nodes is connected when at least one route exists between them (Barthelemy2011), the L-space also constitutes a better choice for the construction of the GMN.This is mainly due to the fact that the P-space does not preserve the spatial structure ofthe network, which suggests a crucial perspective for the research purpose of this study.

Fig. 2 a Spatial distribution of the GMN’s 77 isolated ports b The location of the GMN nodes having loops(cases shown at bigger size)


Finally, the choice of the L-space representation in this study complies with theresearch practice (Barthelemy 2011), where the P-space representation is met in railnetwork applications (Sen et al. 2003), while the L-space is met in maritime (Hu andZhu 2009) and airline (Wang et al. 2011) network applications.

Each Greek port Pi (i=1,…,229) (Fig. 1a), representing in the physical space acontinuous seaside geographical (urban or regional) area, is represented in the L-spaceby a node (Pi→vi) vi∊V(G), which is located at the barycenter’s coordinates (latitude,longitude) of each port’s area. The existence of a direct shipping connection betweenthe pair of ports (vi,vj), i≠j=1,…,229, is represented by an edge eij∊E(G) and it is drawnas a linear segment (Fig. 1a). The length of each edge expresses the geodesic distance,measured in nautical miles, between a pair of nodes (ports) vi,vj∊V(G).

For applying a further step of analysis, the maritime network was considered,additionally to edge-, also node-weighted (Tsiotas and Polyzos 2013b), implying thateach node has some characteristic values describing a set of socioeconomic attributes.The Graph Theoretical models of this article are illustrated by using the Gephi networkmanipulation software (Bastian et al. 2009).

The available structural data was organized to a binary D229×229 (Diestel 2005) andto a distance-weighted adjacency matrix W229×229 (Tsiotas and Polyzos 2013a). Thecoordinates of each Greek port vi∊V(G) were drafted from the Google Maps site [www.google.gr/maps?hl=el].

The socioeconomic data describe aspects of the passenger and commodity traffic perport, referring to the volume of arrivals (AR) and departures (DEP), measured innumber of passengers, and of product package loads (LD) and unloads (UNLD),measured in number of packages. These data (AR,DEP,LD,UNLD) were seasonallyrecorded per Greek port, for the years 2005–2006 (ESYE 2008) and were edited toconstitute mean differences between summer and winter values, as they are shown inrelation (1), where the variable X belongs to the set {AR, DEP, LD, UNLD}, the A set isdefined as A={2005,2006}, the index i refers to the number of port and the symbol “T”indicates a tourism variable.

XT ¼ vif g ¼ 1

2⋅

Xp∈A

xsummer;pi−xwinter;pi� �( )

ð1Þ

The mathematical formula of relation (1) expresses the increase in the GMN trafficinduced by the summertime tourism activity in Greece and it is used to elect tourisminformation from traffic data that include information about both the inhabitant trafficand tourism traffic.

Let consider that the passenger traffic in the winter is expressed by the sum Pw=Iw+Tw, where the term “I” refers to inhabitant traffic and “T” to tourism. Accordingly, PS=IS+TS expresses the relation corresponding to the summer period. We define that theinhabitant traffic in the GMN regions is constant and that it can satisfactorily bedescribed from the winter traffic (Iw=IS≡Iw).

Such a convention seems rationale for two reasons. The first is based on theconsideration that the transport traffic, covering the needs for living of the GMN’sall-year inhabitants, is not greater in summer than in the winter. Any extra summertimetransportation activities conducted from the all-year inhabitants has also a tourism sign.


http://www.google.gr/maps?hl=el

http://www.google.gr/maps?hl=el

Second, the Greek citizens that do not reside in the GMN’s regions, but they locomotein the summertime to the GMN for occupation purposes they can be considered as partof the tourism activity, since they provide services to tourism and they simultaneouslycontribute to the tourism’s consumption.

Within this conceptual framework, the difference PS–PW elects tourism informationfrom the available traffic data, which is latent whether considering each of the terms PS,PW, individually.

In accordance to the previous consideration, the differences calculated on thepackage traffic data also correspond to tourism information. Moreover, such differencesare capable to capture also the indirect tourism information, referring to the additionalsupplies serving the tourists arriving to their destinations by airplane, which are notincluded in the passenger traffic recorded by the harbor authorities, since trade activityamong the GMN’s regions is conducted by sea.

Finally, the existence of seasonality in the available socioeconomic GMN databrings into the conversation the question whether the topology of this maritime networkis seasonally dependent. The GMN’s topology can be considered as a snapshot of thefree market that depends on the strategic plans of the shipping enterprises activated inthe national maritime network. Under this perspective, seasonality, obviously affectsthe topology of the GMN and this observation suggests a limitation of this study.

Nevertheless, this limitation does not suggest a considerable concern, due to the factthat the national maritime market is regulated by the Greek state, within the frameworkof applying regional policy, by subsidizing the unprofitable shipping routes. Under thisconsideration, the topology of the GMN can be considered indifferent to seasonality,implying that it is developed on a fixed set of profitable and unprofitable shippingroutes, where seasonality only affects the volume of network traffic that is alreadybeing captured by the available data.

2.3 Graph Metrics and Complex Network Analysis Measures

The Network Theoretical measures and metrics used for the analysis of the GMN arebeing presented briefly at the following paragraphs:

Graph density ρ is the fraction of the number of the Graph edges |E(G)|=m (existingconnections) to the number of the possible connections (Diestel 2005). Thismeasure represents the probability to meet in the GMN a connected pair ofnodes vi,vj ∈ V(G), via a direct shipping connection eij∊E(G), and operates asan index of the total connectivity of the GMN. The mathematical expression ofgraph density is shown at relation (2), where Gcomplete refers to the complete orperfect matching graph.

ρ ¼ E Gð Þj jE Gcomplete

� �� ¼ E Gð Þj j= N Gð Þj j2

� �¼ m=

n2

� �¼ 2m

n⋅ n−1ð Þ ð2Þ

Node Degree k (Diestel 2005) is the number of the adjacent edges to a given node,expressing its communication potential. This measure counts the number of the directshipping connections or, more generally, of the different shipping routes originating froma given port of the GMN, expressing the connectivity of each GMN’s port. The Average


Network’s Degree ⟨k⟩ is the mean value of all node degrees of the network set V(G), asshown at relation (3), expressing the average number of routes originating from the ports ofthe GMN.

kh i ¼ 1

V Gð Þj j ⋅XV Gð Þj j

i¼1

k ið Þ ¼ 1

n⋅Xi¼1

n

k ið Þ ð3Þ

Node Closeness Centrality (local) (Cc) (Koschutzki et al. 2005) computes the totaldistance d(vi,vj) along the shortest paths from a given node v∊V(G) to all the othersvi∊V(G) in the network, within a bond (connected) component (local measure), ex-pressing the node’s reachability or general accessibility cost of overcoming spatialseparations among places (Tsiotas and Polyzos 2013a). Closeness centrality is com-puted according to relation (4), and it can be either binary, when the adjacency matrixD229×229 is used, measuring number of steps away, or weighted, when nauticaldistances are considered to the calculations.

CC

i ¼ 1

Vj j−1 ⋅XVj j

j¼1;i≠ jdi j ¼ 1

n−1⋅Xj¼1;i≠ j

n

di j ¼ di ð4Þ

The measure of closeness centrality expresses the average distance that a node hasagainst the set of the other nodes of the network, calculated in the network’s metricspace. The physical interpretation of this measure corresponds to the average length ofthe shipping routes originating from a given GMN’s port against all the possibleconnected port destinations.

Node Betweenness Centrality (local) (Cb) (Koschutzki et al. 2005) captures thevolume of communication of a node in comparison to others, within a bond component(local). Node betweenness is the fraction of all shortest paths σ(k) in the network thatcontain a given node k, to the total number of all the shortest path in the network σ, asshown at relation (5). In the physical GMN’s metric space, the betweenness centralitymeasures the volume to which a port constitutes an intermediate station against allpossible shipping routes in the GMN. This measure may attain both binary andweighted calculations, according to the distance metric used for computing shortestpaths (Tsiotas and Polyzos 2013a).

Cb

k ¼ σ kð Þ=σ ð5Þ

The Clustering Coefficient (local) (Latapy 2008; Wang et al. 2011) expressesthe probability of meeting linked neighbors around a node (Latapy 2008),which is equivalent to the number of triangles shaped by a given node, whichis equal to the number of its connected neighbors E(v), divided by the numberof the total triplets shaped by this node, as it shown at relation (6) (Wang et al.2011). The measure is considered local, because calculations occur within bondcomponents, and can also have a distance weighted expression describing theaverage “intensity” (Onnela et al. 2005) of triangles around a node, using theweighted adjacency matrix. In the GMN’s space, the clustering coefficientexpresses the probability of meeting shipping connections among the neighbors


of a port and it operates as an index of the local maritime (neighborhood)connectivity around a port.

Cv ¼ triangles vð Þtriplets vð Þ ¼ E vð Þ

kv⋅ kv−1ð Þ ð6Þ

Modularity (Newman 2006) quantifies the level to which a network may be subdividedinto communities (sub-networks of non-overlapping groups of nodes), whichmaximizes thenumber of within-group edges and minimizes the number of between-group edges.Newman’s (2006) formula formodularity is shown at relation (7), where gi is the communityof node vi∊V(G), [Aij - Pij] expresses the difference of the actual minus the expected numberof edges falling between a particular pair of vertices vi,vi∊V(G), δ(gi,gj) is an indicatorfunction, returning 1 when gi=gj, and 1/2m is a conventional factor. In terms of physicalinterpretation, modularity expresses the cohesiveness of the GMN, implying the level towhich its shipping routes can serve global or local maritime transportation needs.

Q ¼ 1

2m⋅Xi; j

Ai j−Pi j

� �⋅δ gi; g j

ð7Þ

The Average Path Length ⟨l⟩ (Wang et al. 2011) of a network expresses the meanlength d(vi,vj) of all shortest paths in the network, as shown at relation (8). This measuremay also attain binary or weighted form, depending on the respective form of theadjacency matrix used in the calculations. The physical interpretation of this measurecorresponds to the average length of the shipping routes in the GMN, quantifying thescale of distance that this maritime network was developed to serve and thus thetransportation capability of the GMN.

lh i ¼ 1

n⋅ n−1ð Þ ⋅X

vi;v j∈V Gð Þd vi; v j� � ð8Þ

Finally, the Degree Distribution (Barabasi and Albert 1999) P(k) is a mathematicfunction expressing the frequency of nodes nk in connection to the k, as shown atrelation (9). In terms of physical interpretation, the degree distribution enumerates thenumber of ports that have a certain number of shipping routes.

p kð Þ ¼ Vk Gð Þj j ¼ nk ; Vk Gð Þ ¼ vi∈V Gð Þjk við Þ ¼ kf g ⊆V Gð Þ ð9Þ

2.4 Statistical Tools

GMN is considered both node- and edge-weighted, where further statistical socio-economic variables of dimension |V(G)|=229 can be adjusted, extending the informa-tion capacity of the model. These statistical variables describe some non-structuralattributes for the maritime network and thus allow proceeding into an empiricalanalysis, utilizing some tools of descriptive statistics, correlation analysis, statisticaltesting and fitting techniques.

At the following, Pearson’s bivariate coefficients of correlation (Norusis 2004;Devore and Berk 2012) are calculated, in order to detect any existence of linearrelations between pairs of variables. The mathematical formula of the correlationcoefficient is shown at relation (10), where cov(x,y)≡sxy stands for the covariance of


variables x,y andffiffiffiffiffiffiffiffiffiffiffiffivar xð Þp

≡sx ,ffiffiffiffiffiffiffiffiffiffiffiffivar yð Þp

≡sy are their respective sample standarddeviations. Pearson’s coefficient of correlation ranges within the interval [−1,1], ex-pressing a perfect linear relation in cases |rxy|=1 (Devore and Berk 2012).

r x; yð Þ≡rxy ¼ cov x; yð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivar xð Þ⋅var yð Þp ≡sxy= sx⋅sy

� � ð10Þ

In order to detect randomness, the Kolmogorov-Smirnov (K-S) one-sample test(Massey 1951; Conover 1980; Norusis 2004) is applied, comparing the observedvariable’s cumulative distribution with the Poisson’s theoretical distribution. Thealgorithm of the Kolmogorov-Smirnov one-sample test first sorts the observations intoascending order, then it estimates the Poisson’s parameter λ from the data (whichequals to the mean value), then it computes the theoretical cumulative Poisson’s

distribution bF xð Þ on the data having the estimated λ, after it calculates the cumulative

differences between the theoretical and observed distributions bF xi−1ð Þ −F xi−1ð Þ , and,finally, it computes the Z-score of the test from the largest difference (in absolute terms)between the compared distribution functions. The two-tailed significance level isestimated using the first three terms of the Smirnov’s (Smirnov 1948) formula.

Finally, a linear regression analysis (Norusis 2004; Hastie et al. 2009) is applied, inorder to detect the level to which a set of predictor variables contribute to describe thevariability of a dependent variable’s data. The linear regression algorithm that is used isthe Backward Elimination Method (BEM) (Norusis 2004; Hastie et al. 2009), whichstarts with the full model, including all the predictors, and provides a sequence ofmodels Yk, where the most insignificant predictors are removed in succession, one perloop, among these that have statistical significance (p-value) p >0,1. Given the set ofindependent variables Xn={X1, X2,…, Xn} then the sequence of the BEM dependentvariables (Yk)k≥0 is described by relation (11).

Ykð Þk∈ 1;…;nf g⊆;

Y k ;¼;Xn−kþ1

i¼1

bi⋅X i þ ck ;

Xn;¼; X 1;X 2;…;X nf g;X i; ∈;

Xn−kþ1;Xn−k ;¼;

Xn−kþ1; −; X p

� ;X p; ∈;

Xn−kþ1; :;P; b X p

� � ¼ 0� �

;¼;max; P bi ¼ 0½ �≥0; 1f g

8>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>:

ð11Þ

The standardized coefficients calculated from the Backward Elimination processindicate the participation of each predictor variable to the BEM model (Norusis 2004;Hastie et al. 2009).

2.5 Methodological framework

This subsection describes the methodological framework that is used for managinglocal and global measures and it also describes the parts composing the empirical


analysis. The conceptual framework of the applied methodology is illustrated in thediagram of Fig. 3, indicating that the topological and spatial analysis of the GMN isbased on the decomposition rationale.

In general, the GMN constitutes a disconnected network consisting of a set of n=7sub-networks (component groups). In topological terms, distances among disconnectedcomponents are usually defined as infinite (Koschutzki et al. 2005), fact that electsissues regarding the definition of the global network measures and especially of thosethat are distance-defined.

According to Koschutzki et al. (2005), the measures that are defined by theenumeration of cases, such as the betweenness centrality, which counts the relativenumber of shortest paths passing through a node, do not suffer from this problem.Based on this interpretation, network measures such as the node degree, which countsthe number of connections, the clustering coefficient, which counts the number ofrelative triangles, and the graph density, which counts the number of relative edges in anetwork, they also seem to be well defined in the global GMN.

In their work, Koschutzki et al. (2005) discuss the approaches dealing with insuf-ficient connectivity, depending on the level of the desired accuracy. Taking underconsideration that this study is already submitted in a set of conventions capable insmoothing the additional level of accuracy of the most sophisticated connectivity repair

Fig. 3 The methodological framework that is used for the analysis of the GMN


methods, this paper applies the two of the simplest methods for dealing with GMN’sdisconnectivity, which are called, in this paper, the local restriction method (LRM) andthe proportional conversion method (PCM). This treatment, of moving gradually tomore difficult techniques, complies with the common practice of dealing with data sets(Norusis 2004), since the applicability of these methods will be evaluated by the resultsof the empirical analysis.

According to the methodological framework of Fig. 3, the network measures and thedescriptives of the GMN are calculated locally (per component), where all the cases arewell defined, and, afterwards, they are being converted into global GMN sets. Whenthe LRM is used, the local measure sets are merged into global sets, named unweightedglobal sets (WGS), filling with zeros the empty cases. Whether applying the PCM,each local measure is weighted according to the size of the GMN’s component that itbelongs and then all the results are placed into global sets, named weighted global sets(WGS), filling with zeros the empty cases.

The gradient global GMN measures are converted using the LRM, in order to becomparable with measures of other networks. The vector GMN measures, whichconstitute variables consisting of 229 elements, are converted using the LRM orPCM, depending on the analysis. The K-S test and the fitting analyses are applied todegree variables calculated on UGS, due to the universality attribute of the node degree.On the other hand, GMN variables participated to the correlation and BEM analyses arecalculated on both UGS and WGS, for comparing their results.

Finally, the results produced using the methodological framework of Fig. 3 are beingevaluated and compared, in order to generally provide a feedback for debugging andupgrading the methodological process for future applications.

3 Results and Discussion

3.1 Structural and Topological Analysis

3.1.1 GMN Measures and Descriptives

The GMN is a maritime transportation system that connects 229 ports among regions ofGreece. According to the national 2011 census (ELSTAT 2011), the population of themunicipalities of the GMN’s ports is 2’595’272 people, representing an amount of24 % of the total country’s population (10’815’197). Out of the 51 Greek prefectures,35 have direct access to one of these 229 GMN ports, referring to an amountof 87 % of the country’s population. This system is interconnected with 231bidirectional transportation routes, constituting an undirected Graph Theoreticalmodel G(n=229,m=231).

Table 1 shows the network measures describing the GMN in comparison to somecharacteristic measures of the World Maritime Network (WMN), as described byBarthelemy (2011), and in comparison to the corresponding measures of the Aegeanand Ionian components, considered either as connected components or as geographicalsub-regions (including isolated nodes, dipoles and small components). The maximumnode degree of the GMN is kmax(G)=19, belonging to the port of Piraeus that isconsidered a hub (O’Kelly 2014), and the minimum is kmin(G)=0, describing the


existence of isolated nodes in the network. The average GMN node degree is ⟨k⟩=2.017≈2 and excluding the isolated nodes is ⟨k⟩′=3.42. The average GMN edge lengthis 40.89nm and the total length (the sum of all edges) is 9’136.91nm.

These distance values describe the “spatial impedance” or cost that should beovercome in order to produce network flows. In microeconomic terms, the average

Table 1 Comparative table among the network measures of the GMN, the Aegean and the Ionian compo-nents and of the World Maritime Network (WMN)a

Metric/ Measure Unit GMNb Aegean Ionian WMNa

Component Sub-Region

Component Sub-Region

No. vertices # 229 112 184 18 45 878

No. edges # 231 194 202 21 28 7955

Max. degree # 19 19 19 4 4 ~100

Min. degree # 0 1 0 1 0 1

Average degreec # 2.017 N/Ae 2.196 N/A 1.244 N/A

Average degreed # 3.42 3.464 3.285 2.333 1.931 ~9

Average edge length nm 40.89 42.65 39.96 30.73 30.67 N/A

Total length nm 9’580.98f 8’182.47 8’392.37 1’084.41 1’188.61 N/A

Average distance-weighteddegreec

nm 79.80 147.13 130.99 46.32 59.10 N/A

Graph densityc net 0.009 N/A 0.012 N/A 0.028 N/A

Graph densityd net 0.02 0.031 0.027 0.137 0.069 0.0206

Connected components # 7g 1 66 1 22 1

Isolated nodes # 77 Ø 61 Ø 16 Ø

Nodes with loops # 12 8 11 1 1 N/A

Network diameter # 15 15 15 8 8 N/A

Network diameter’s distance nm 624.14 624.14 624.14 245.84 245.84 N/A

Average clustering coefficientc net 0.186 N/A 0.328 N/A 0.488 N/A

Average clusteringcoefficientd

net 0.345 0.32 0.328 0.213 0.488 ~0.4

Average path lengthd # 5.317 5.38 5.362 3.366 3.262 ~3.6

Average path lengthd nm 217.39 229.46 214.10 103.44 99.88 N/A

Average nearest neighborsdegreed

# 5.88 6.15 5.93 4.97 4.84 N/A

Modularityd net 0.764 0.599 0.708 0.422 0.655 N/A

a Source: (Barthelemy 2011)bAverages calculated on unweighted global setscCalculations included isolated nodesdCalculations without isolated nodeseN/A: Not AvailablefThousands separatorgAfter the topological grouping


edge distance represents the minimum economic effort that a port (node) needs tooccupy in order to conduct one degree of communication and, in macroeconomicterms, the sum of all edges in the network describes the total economic difficulty thatGreece is daily facing in promoting maritime movements.

The GMN’s average weighted degree is 79.80nm representing the mean distance ofa node to its neighbours. The ratio 79.80km/2.017=39.56nm, expressing the meanneighborhood distance, is smaller to the average edge length (39.56nm<40.89nm),implying a better communication potential of the GMN in neighborhood scale.

GMN is not a dense network, having probability to meet a connection between ports(graph density) 0.009. Whether excluding the isolated nodes, the GMN’s density (ρ′GMN=0.02) is similar to the WMN’s density (ρWMN=0.0206).

According to the foregoing topological grouping, the GMN consists of 7 componentgroups, including the group of 77 isolated nodes (Fig. 1b). The two largest GMNcomponents are the Aegean (comp#1) and the Ionian (comp#2) components, while theother thinner (including 5 bipolar) components serve local transportation needs. As itwas previously mentioned, the disconnectivity of the GMN is a result of competitionexisting “within” the same transportation mode and “between” different transportationmodes, but this issue is not being further examined within the scope of this paper.

Figure 4 shows the pile bar-charts describing the performance of each GMNcomponent to a group of normalized reference measures (number of nodes and edges,average binary and weighted degree, diameter, density, modularity, clustering coeffi-cient and average path length), calculated on UGS. An interesting observation here isthat the cases of the bipolar component (#6) present a standardized overall perfor-mance, implying that the topology of the dipoles is independent to distance. Also, theGMN’s large components present low scores in the measures of density and clusteringcoefficient.

Figure 4 also shows that the group with the isolated nodes (comp#7) constitutes acomponent of null topology. Nevertheless, this component has a positive trade activityin the GMN, fact that justifies the choice of considering it as a topological component.The isolated ports are spatially distributed according to Fig. 2a, covering an amount of

Fig. 4 Bar-charts showing normalized measures of the 11 GMN components


77/229=33.62 % of the GMN node set V(G). This status implies that a significantamount of the GMN ports, the majority of which is central-west located, seem to havelocal activity, probably referring to fishery, yacht or marinas services, or to some short-scale trade and services.

Next, a dozen (5.3 % of the total) GMN ports are loop-nodes, meaning that thesenodes are also self-connected. Figure 2b shows the spatial distribution of these nodes,implying, according to the majority of cases, that the loop attribute is an insularcharacteristic of the distant ports that present a difficulty to sufficiently connect to themainland.

Finally, Table 1 shows that the GMN’s average clustering coefficient is ⟨c⟩′=0.345(excluding the isolated nodes), implying that the probability of meeting linked neigh-bors around a port is 34.5 % and that the average path length, expressing theconvenience of travelling in a given network, is ⟨l⟩′=5.317 steps of separation or217.39nm. These measures are useful in detecting the GMN’s typology (Wang et al.2011) that is examined at the following.

However, it is very interesting that the average clustering coefficient of the GMN isclose to the value of the average clustering coefficient of the WMN, implying a kind ofcohesion in the structure of maritime networks, regardless of scale. Finally, the networkmodularity, expressing the ability of the GMN to develop communities, is significant(Q=0.764), implying that the GMN has polycentric potentials.

3.1.2 GMN Pattern Recognition

This paragraph examines the typology of the GMN’s structure. Table 2 (Wang et al.2011) helps initializing this procedure and, although it provides a loose calibration, itallows classifying the undetected network among five reference networks, according toits size level in average path length ⟨l⟩, clustering coefficient ⟨c⟩ and degree distributionp(k).

The GMN has an average path length almost equal to the 1/3 of its network diameter(⟨l⟩≈1/3·d(G)) and a clustering coefficient almost 30 times greater than a randomnetwork (⟨c⟩≈30⋅⟨c⟩rand). Under this rationale, GMN can be considered, according tothe loose grading of Table 2 (Wang et al. 2011), to have a short average path length anda large clustering coefficient, excluding the case to suggest a random network.

According to Barthelemy (2011), an Erdos-Renyi (Erdos and Renyi 1959) randomnetwork has a clustering coefficient ch ie1�n

. By calculating the ratio 1�nfor the GMN,

the result is far from representing a random network, since 1�n ¼ 1

�229

¼ 4:36⋅10−3≠

Table 2 Characteristics of pattern networks (Wang et al. 2011)

Network Average path length, ⟨l⟩ Clustering coefficient, ⟨c⟩ Degree distribution, p(k)

Regular network Long Large Point to point

Random network Short Small Binomial or poisson

Small-world network Short Large Exponential or power-law

Scale-free network Short Large Power-law

Real network Short Large Similar power-law


ch iGMN ¼ 0:345 . This result is approximately 80 times greater than the random corre-sponding score ⟨c⟩rand=4.36⋅10−3, excluding the existence of randomness in the GMN.

This result is being verified by applying the one-sample Kolmogorov-Smirnov t-testto the degree set of the GMN nodes. Given that a random pattern is classicallydescribed by the Poisson’s distribution (Norusis 2004, Norusis 2005), the K-S test isapplied to test whether the degree of the GMN’s nodes follow the Poisson distribution.The results of the one-sample K-S t-test are shown in Table 3. Unlike much statisticaltesting, this test indicates good fitting when results are insignificant (Norusis 2004).

According to Table 3, the testing result is strongly significant, meaning that thePoisson distribution is not good fit for the GMN’s degree distribution and thus GMNdoes not constitute a random network.

After the foregoing analysis and according to Table 2, the typology of the GMNmaybe detected depending on the pattern of the GMN’s degree distribution. In order toclassify GMN among the categories of scale-free, small-world and real network, thedegree distribution should be checked whether it follows a power-law or an exponentialdistribution. Figure 5 shows the power-law (log-log) fitting curve, where the coefficientof determination (R2) (Norusis 2004) indicates that this model can almost perfectlydescribe the variation of the GMN’s degree distribution data. Besides, GMN cannot bea small-world network since its binary diameter consists of 15 steps, which is far evenfrom the classical diameter of the “six degrees of separation” that describe a giantsmall-world network (Easley and Kleinberg 2010).

The almost perfect fitting power-law status, in conjunction with the fact that the power-law parameter -b=−1.745 does not seem to be considerably far from the typical interval 2,1<|b|<4, which describes cases of scale-free networks (Barabasi and Albert 1999), impliesthatGMN tends to adopt a scale-free structure. Moreover Fig. 5 shows clearly that a pair ofpower-law curves fits in the data. The peak point appears at the degree of 2.5 (between 2 and3), implying that the GMN is better described by a dual scale-free dynamic, one concerningports of low degree (up to 3) and the other of high degree (greater than 3).

Detecting scale-free characteristics in the structure of GMN it may be related to thefact that the sea constitutes a transportation medium that lacks of morphologicalanomalies, providing by this way a flat surface for promoting unhindered transporta-tion activities. Under another aspect, these scale-free trends, captured by the fittingprocess, may interpret a kind of indifference of the shipping enterprises to the nauticalmile distances, meaning that the time spend by passengers inside the ships, during thelasting shipping trips, seems to be sufficient in producing consumptions able to surpassthe travel distance costs and thus to be profitable to the shipping enterprises.

Table 3 One-SampleKolmogorov-Smirnov Testa

aVariable: DEGREEbTest distribution is PoissoncCalculated from data

GMN

N - 229

Poisson parameterb, c Mean 2.02

Most extreme differences Absolute .203

Positive .203

Negative -.077

Kolmogorov-Smirnov Z 3.076

Asymp. Sig. (2-tailed) .000


The existence of scale-free attributes in the GMN seems to be consistent to thestatement of Barthelemy (2011), according to which geographical constraints appearless severe for cargo ship and thus for maritime connections, since the existence ofanomalies disqualifies the creation of long links, favoring more the compensation oflarger degrees than of costly long links in a network.

3.2 Empirical Analysis

This paragraph applies an empirical analysis to the GMN, comparing the foregoingstructural and topological attributes with the available socioeconomic GMN data, byusing Pearson’s bivariate coefficients of correlation and the linear regression BackwardElimination Method (BEM), according to relations (10) and (11), respectively. Thevariables included at the correlation analysis are shown in Table 4.

The available (except the population) data correspond to a pre-crisis period, whereGreece was still utilizing a “healthy” developmental economic pattern. In particular,these data are referenced to a couple of years prior the recent world economic crisis,which was originated from the USA at 2007 and it was starting to influence Greece bythe next year, at 2008, concluding to the renowned Greek (for many analysts European)Economic Crisis that officially initiated in Greece at 2010 (Polyzos et al. 2013b).

3.2.1 Correlations

The results of the correlation analysis are shown in Tables 7 and 8, where variables arecalculated on UGS and WGS data, respectively. Table 7 shows that the binary topolog-ical variables of the GMN are highly and significantly correlated to their homologousweighted variables, having coefficients of correlation (2-tailed significant at the 5 %level) r(CB

bin,CBw)UGS=0.803, r(C

Cbin,C

Cw)UGS=0.968, r(Clustbin,Clustw)UGS=0.791.

Similar results (also significant at the 5 % level) are also captured in Table 8, wherer(CB

bin,CBw)WGS=0.804, r(C

Cbin,C

Cw)WGS=0.968, r(Clustbin,Clustw)WGS=0.855.

This observation implies that the structure of GMN is highly indifferent to distance, factwhich also comes to an agreement with Barthelemy’s (2011) statement regarding the loosergeographical constraints empirically observed in cargo ship networks. Distance seems toaffect GMN’s reachability (CC) in an amount of 3.2 %, the structure of intermediate routes

Fig. 5 Log-log power-law fitting curves (one curve on the left and two curves on the right side) of the GMNdegree distribution data


Table 4 Variables participating in the empirical analysis

Variable Code Description Measure/Unit Reference

Topological and spatial variablesa

DEG The degree of each port in the GMN # ofconnections

(Diestel 2005)

CB_binb Betweenness centrality – binary*. Shortest pathspercentage

(Koschutzki et al.2005)

CB_wc Betweenness centrality – distance weighted** Shortest pathspercentage

(Brandes 2001)

CC_binb Closeness centrality – binary # of steps (Diestel 2005),(Koschutzkiet al. 2005)

CC_wc Closeness centrality – distance weighted Nautical miles (Koschutzki et al.2005)

CLUST_binb Clustering coefficient (Probability of meetingconnected neighbors)

Probability (Watts and Strogatz1998)

CLUST_wc Clustering coefficient (Intensity of meetingconnected neighbors)

Probability (Onnela et al. 2005)

MOD Modularity Dimensionlessnumber

(Newman 2006)

ACC_ZONE Accessibility Zone: The area of the region that hasaccess to each port.

km2 (ELSTAT, 2011)

Socioeconomic variables

POP Port Population: The population of the urban unitswhere the ports belong.

# of people (ELSTAT, 2011)

REG_POP The population of the prefectures where the portsbelong.

# of people (ELSTAT, 2011)

A_SEC The participation to the national primary sector’sGDP of the prefectures where the ports belong.

percentage (Epilogi 2006)

C_SEC The participation to the tertiary sector’s GDP of theprefectures where the ports belong.

percentage (Epilogi 2006)

ART Tourism arrivals for each ports per prefecture(considered as differences on summer-winterdata)

# of people (ESYE, 2008)

DEPT Tourism departures for the ports per prefecture(considered as differences on summer-winterdata)

# of people (ESYE, 2008)

LDT Tourism package load for the ports per prefecture(considered as differences on summer-winterdata)

# of packages (ESYE, 2008)

UNLDT Tourism package load for the ports per prefecture(considered as differences on summer-winterdata)

# of packages (ESYE, 2008)

a Variable calculated based on the GMN model’s datab At binary measures the distances are considered as number of network stepsc Distance weighted measures calculate real distances from the map (nautical miles)


(CB) in an amount of 19.7 % and the state of neighborhood connectivity (the clusteringcoefficient) in an amount of 20.9 %.

If such indifference suggests an aspect of the scale-free property in a spatial network,then the coefficient of correlation between binary and their homologous structuralnode variables may operate as an alternative scale-free indicator. This assumptionsuggests a methodological recommendation and a topic of further research that shouldbe empirically tested on various networks.

The results in Table 7 also show that the tourism activity, as it was previouslydefined in relation (1), in the GMN is degree- and intermediacy-controlled, due to the(significant at the 5 % level) correlations r(DEGUGS,AR)=0.602, r(DEGUGS,DEP)=0.594 and r(CB

bin/UGS,AR)=0.699, r(CBbin/UGS,DEP)=0.700, meaning that the GMN

ports, considered as central in terms of connectivity and intermediacy, are also morepopular in receiving passenger flows. The respective scores for the WGS case (Table 8)are r(DEGWGS,AR)=0.608, r(DEGWGS,DEP)=0.599 and r(CB

bin/WGS,AR)=0.699,r(CB

bin/UGS,DEP)=0.700, which are also significant at the 5 % level.Comparing the (significant at the 5 % level) correlation’s results r(CB

bin/UGS,AR)=0.699 and r(CB

bin/UGS,DEP)=0.700 with their homologous distance-weighted r(CBw/

UGS,AR)=0.442 and r(CBw/UGS,DEP)=0.440 (Table 7), we can see that they are loosen

from the binary to the distance-weighted case. The respective WGS scores (Table 8) arer(CB

bin/WGS,AR)=0.699 and r(CBbin/WGS,DEP)=0.700 and their homologous distance-

weighted r(CBw/WGS,AR)=0.443 and r(CB

w/WGS,DEP)=0.440, which are alsosignificant at the 5 % level. This implies that, although the GMN’s topology ishighly indifferent to distance, the GMN’s tourism flow production mechanism, whichis controlled among the other factors and by the individuals’ willingness to visit atourism destination, takes distance more seriously for the conduct of intermediacy.

Next, according to Table 7, distance seems also to present a statistically significant(at the 10 % level), but low, contribution to the GMN’s product unloading (UNLD), asit is captured by the coefficient r(CC

w/UGS,UNLD)=0.156. The respectiveWGS score isr(CC

w/UGS,UNLD)=0.155, which is significant at the 10 % level. This implies thatdistant GMN ports show greater product demand than the others. This result turnsstatistically insignificant in the binary (both for the UGS and WGS) cases of closenesscentrality, interpreting that this slight increase in trade demand, which is captured in theweighted case, depends only on distance and not on the GMN’s topology.

Another set of interesting observations concern the correlation results among thepopulation (POP, REG_POP) and economic variables (A_SEC, C_SEC). According toboth the UGS (Table 7) andWGS (Table 8) cases, the ports’ population (POP) seems tocontrol the variability in the data of both the topological and traffic GMN’s variables.

In particular, according to the Table 7 (UGS variables), the variability in the data of theGMN ports’ population is reflected in an amount of 23.5 % in the variability of the GMN’sconnectivity (DEG), in an amount of 29.2 % in the variability of the binary betweennesscentrality (CB

bin), in an amount of 17.2 % in the variability of the distance-weightedcloseness centrality (CC

w), and in an amount of over 30 % in the variability of theclustering coefficients, where all results are significant at the 5 % level. Similar scores arealso being observed in the Table 8.

On the other hand, the variability in the data of the GMN regions’ population seems notto be reflected in the GMN’s topology, but only in the GMN’s economic activity(A_SEC,C_SEC) and traffic (ART,DEPT, LDT,UNLDT). This observation is also consistent


in the scores of Table 8. According to this observation, the GMN’s regions with highpopulation are more likely to present specialization to the tertiary sector (C_SEC) and,inversely, they are less likely to present specialization to the primary sector (A_SEC). Thisillustrates that the economic basis of the GMN is oriented to providing tourism services.

Moreover, taking under consideration that the primary sector provides supplies servingfeeding needs and, generally, needs of tourism consumption (Polyzos et al. 2014), then thenegative correlations r(POP,A_SEC) and r(REG_POP,A_SEC) illustrate that the agricul-tural productivity is an externality in the GMN’s activity, implying that the GMN operatesas a huge market of agricultural goods for serving the feeding needs of tourism.

In terms of regional policy, the previous observation comes to an agreement with thework of Polyzos et al. (2014), which they have noted that the Greek state adoptsdisconnected strategies for the agricultural and tourism development, preferring aspatial separation of their activities that probably loosens the competition and com-plexity and gives the opportunity to non tourism-based local economies to grow. Theyalso noted that agro-industries prefer locations that establish easy access to rawmaterials and to effective supply chains for promoting their products rather than tocentral places of great endogenous markets.

The case of GMN, being interpreted as a market of agricultural goods, verifies thisobservation. According to both Tables 7 and 8, the correlations referring to the variable of theprimary sector’s participation (A_SEC) are, in all the cases related to the GMN’s topologyand traffic, either negative or insignificant, implying the separation of the GMN’s activitiesfrom the agricultural productivity. Policies aiming to link tourism services with agriculturalproductivity constitute a developmental issue that the Greek regional policy should focus on,in order to promote the developmental dynamics of the country and simultaneously toupgrade the quality of the tourism services, by providing local produced goods.

3.2.2 Linear Regression

Linear Regression Analysis (BEM model) is applied for detecting the level to which aset of predictor variables contribute in common to the description of the variability of adependent variable’s data. For constructing the BEM model, the degree of the GMN’sports (representing the GMN’s connectivity) was chosen to be the dependent variable Y,while all the other 16 variables of Table 4 were entered in the model Y ≡ DEG =f(X)=f(X1, X2,…, X16), as the predictor variables.

Table 5 shows the results of the BEM analysis considered for both the UGS and WGSvariable cases. According to Table 5 (model summary), the UGS and WGS models areresulted to the optimummodels after rejecting 9 and 10 insignificant predictors, respectively.Also, in Table 6 the results of the coefficient of determination show that the WGS model isabout 5 %more efficient than the UGS in describing the variability of the response variable(DEG). This interprets that, regarding the conversion of the local network measures intoglobal measures, the proportional conversion method (PCM) performs better than the localrestriction (LRM) for describing the connectivity of the GMN.

According to the Table 6, both the UGS and WGS linear regression models present asimilar picture of the set of the significant predictor variables. These results illustrate that theconnectivity of the GMN is dependent on topological, spatial and economic factors. As it canbe observed, the variability of the GMN’s connectivity (DEG) is described by the variabilityof the betweenness centrality (CB_bin+CB_w) in an amount of 43.5 %, of the closeness


centrality (CW_bin or CW_w) in an amount of 24–28 %, of the clustering coefficient(CLUST_bin) in an amount of 19–23 %, of the number of arrivals (ART) in an amount of30–32 % and of the tertiary sector’s participation (C_SEC) in an amount of 12–21 %.

In particular, the contribution of both the binary and weighted betweenness central-ities to the BEM models is obvious. Ports that intermediate among more maritimeroutes are more likely to present higher connectivity (degree) in the GMN, fact which iscaptured by both the UGS and the WGS models in the BEM analysis. Such an obviousrationale also describes the contribution of the clustering coefficient to the BEMmodels(Table 6). Ports with connected neighbors are more likely to present higher connectivitythan those with non-connected neighbors, implying that such ports are located intoareas of greater maritime activity and socioeconomic interest.

Table 5 Results of the BEM analysis. BEM model summary

Model Loops until optimum model R R2 Adjusted R2 Std. error of the estimate

UGS(a),(b) 9 .822 .676 .666 1.416

WGS(c),(d) 10 .854 .729 .722 .6477

a UGS = Variables calculated on unweighted global setsb Predictors: (Constant), CB _w, CLUST_bin, CC _bin, C_SEC, REG_POP, ART, C

B _bincWGS = Variables calculated on weighted global setsd Predictors: (Constant), CB _w, CLUST_bin, C_SEC, CC _w, ART, C

B _bin

Table 6 Results of the BEM analysis. BEM coefficients

Optimum model Unstandardized coefficients Standardized coefficients t Sig.

B Std. error Beta

UGSa (Constant) −2.154 .558 −3.857 .000

REG_POP −2.039E-07 .000 -.096 −2.333 .021

CB_bin .001 .000 .222 2.611 .010

CB_w .001 .000 .213 3.108 .002

CC_bin .439 .072 .248 6.058 .000

C_SEC 4.166 .799 .211 5.218 .000

ART .373 .067 .322 5.599 .000

CLUST_bin 1.202 .243 .195 4.938 .000

WGSb (Constant) -.755 .251 −3.005 .003

CB_bin .001 .000 .176 2.240 .026

CB_w .001 .000 .259 4.162 .000

CC_w .006 .001 .281 6.911 .000

C_SEC 1.232 .352 .125 3.504 .001

ART .177 .030 .305 5.841 .000

CLUST_bin 2.120 .363 .227 5.844 .000

a Dependent variable: DEGUGS

bDependent variable: DEGWGS


Nevertheless, the case of the closeness centrality does not produce such obvious results.According to the BEM analysis (Table 6), the GMN’s ports with higher average length intheir shipping routes are more likely to have greater connectivity. This result, with theexemption of the port of Piraeus, illustrates an eccentricity attribute of the GMN’s connec-tivity, implying that the GMN connections were developed to connect distant ports. Further,this observation illustrates the tourism ontology of the GMN, where ports having greaternumber of connections seem to be these that they have greater tourism attractiveness, whichthey are also more distant in the GMN’s geographical space.

Further, the presence of the C_SEC variable in the set of the optimum predictors of boththe UGS andWGSmodels implies that an aspect of the GMN’s connectivity, describing anamount of 12-21 % of its variability, is oriented to services’ provision. This observation, inconjunction with the contribution of the predictor ART to both optimum BEM models,describing an amount of 30-32 % of the GMN’s connectivity, illustrates the tourismontology of the GMN, where maritime services seem, in their majority, to serve tourism.

Another remarkable result of the BEM analysis is the negligible contribution of thedemographic parameter (population variables) to the determination of the GMN’s connec-tivity. In particular, the UGS model illustrates a negative contribution (−9.6 %) of theregional population to the GMN’s connectivity, while the WGS none. This, in conjunctionwith the correlation analysis results, implies that the demographic parameter has indirecteffects to the GMN’s connectivity, controlling mainly its topological and spatial character-istics. Additionally, this observation interprets that the GMN’s structure has diachronicallybeen developed to serve transportation needs of wider than national demand, which is alsorelated to the fact that the Greek tourism serves annually great arrivals (Tzannatos 2005;Diakomihalis 2007) of foreign tourists.

Finally, the absence of the variable A_SEC from the set of the optimum predictors ofthe BEM model verifies the observation made in the part of correlation analysis,regarding the separation of the GMN’s activities from the agricultural productivity.Aiming to link tourism services with agricultural productivity, taking under consider-ation that tourism activity consumes agricultural products, suggests a further develop-mental issue, where Greek policy should focus on.

4 Conclusions

This article modeled the Greek Maritime Network (GMN) as a non-directed GraphG(V,E),in the L-space representation, having |V(G)|=n=229 vertices and |E(G)|=m=231 edges, andanalyzed a set of its structural and socioeconomic characteristics in terms of ComplexNetwork Theory. The GMN corresponds to a national maritime transportation system that isdriven by different characteristics than the respective international and global maritimenetworks, introducing a different research perspective to this article. Such characteristicsrefer to the absence of economies of scale in the GMN, to its disconnectivity, beinginterpreted as a result of the existence of competition within the same transportation modeand of competition between different transportation modes, to the geostrategic importanceand the complex insular morphology of Greece and to the intense seasonality in tourismactivity between the summer period and the remainder of the year.

This paper applied a mixed spatial and topological grouping for studying the GMN’sseparate components and constructed a methodological framework for dealing with


local and global measures. Within this framework, the GMN constitutes a low densitymaritime network that is more cohesive in the scale of neighborhood, showing poly-centric dynamics. The GMN involves ports that occupy the 24 % of the Greekpopulation, provide direct access to the 87 % of the country’s population, that utilizechannels of almost 9’150 nautical miles, that connect pairs of ports with an averagedistance of 40 nautical miles. The 1/3 of the GMN’s node set consists of isolated nodes,having mostly a central-west orientation, implying the existence of a considerable levelof local trade and economic activity. An amount of 5 % of the nodes’ set concerns self-connected nodes that describing distant cases that appear a deficient communicationcapability with the main network body.

The foregoing analysis outlined the existence of a causal structural pattern describ-ing the GMN, by excluding the case this to constitute a random network, and detectedsome scale-free network properties in the structure of GMN, fitting almost perfectly apower-law curve to the GMN’s degree distribution, having the parameter b consider-ably near to the typical Barabasi and Albert’s (1999) scale-free range.

An interesting finding arose from the correlation analysis is the high correlationscaptured between pairs of binary and their homologous distance-weighted node struc-tural variables, driving us to conceptually correspond this status with the GMN’s scale-free properties detected by the fitting process, electing a topic of further research. Thesehigh correlation results interpret a kind of GMN’s structural indifference to distance,probably implying the low contribution of the spatial impedance to the network’sstructure or the GMN’s ability to compensate the distance cost with the interiorshipping consumption conducted during the maritime trips.

Also, the correlation analysis resulted that the GMN’s tourism activity, as capturedby the available data, is degree-controlled, favoring highly connected places for tourismdevelopment. In terms of tourism activity distance seems to affect intermediacy acts,where travel cost is a constraint, and in terms of trade activity distance seems to affectproduct demand, distinguishing a slightly greater demand in the distant GMN ports.

In the part of the linear regression analysis the Backward Elimination Method(BEM) was applied for detecting the level to which a set of predictor variablescontribute in common to the description of the variability of the GMN’s connectivity(degree). The BEM analysis elected a set of topological, spatial and economic predic-tors describing the connectivity of the GMN, referring to the concepts of intermediacy,of closeness, of neighborhood and of tourism activity, where tourism seems to be acritical factor of the GMN’s economic profile. The BEM analysis also elected that,regarding the conversion of the local network measures into global measures, theproportional conversion method (PCM) performs 5 % better than the local restrictionmethod (LRM) for describing the connectivity of the GMN.

Finally, the foregoing analysis elected a developmental address for the Greek regionalpolicy concerning the connection of tourism with agricultural productivity, under theapplication of complementary policies, in order to integrate the developmental dynamicsof the country and simultaneously to upgrade the quality of the tourism services.

The overall study has elected that the effectiveness of complex Network Analysis inmaritime networks is equal to this of other transportation networks, as pointed out byDucruet et al. (2010), utilizing new analytical aspects to the field of port and maritimegeography, in this level of scale, that should be taken under consideration by the transpor-tation policy makers of Greece.


App

endix

Tab

le7

Resultsof

correlationanalysis(variables

calculated

onunweightedglobalsets-UGS)

POP

REG_P

OP

ACC_Z

ONE

DEG

CB(bin)

CB(w

)CC(bin)

CC(w

)A_S

EC

C_S

EC

ART

DEPT

LDT

UNLDT

CLUST

(bin)

CLUST

(w)

MOD

POP

Correl

1.123

.030

.235

a.292

a.078

.110

.172

a-.1

56b

.051

.359

a.360

a.406

a.615

a.303

a.330

a-.0

04

Sig.

.063

.650

.000

.000

.242

.098

.009

.018

.441

.000

.000

.000

.000

.000

.000

.948

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

REG_P

OP

Correl

1-.3

69a

.044

.129

.075

-.049

-.032

-.649

a.272

a.224

a.226

a.194

a.115

-.111

-.112

.081

Sig.

.000

.505

.051

.258

.464

.625

.000

.000

.001

.001

.003

.081

.093

.092

.220

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

ACC_Z

ONE

Correl

1-.1

24-.0

70-.0

40.109

.082

.435

a-.3

88a

-.093

-.093

-,010

.018

-.013

.067

-.047

Sig.

.061

.294

.552

.100

.216

.000

.000

.161

.160

.883

.786

.845

.311

.481

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

DEG

Correl

1.655

a.604

a.441

a.457

a-.0

72.250

a.602

a.594

a.171

a.169

a.256

a.292

a-.0

23

Sig.

.000

.000

.000

.000

.280

.000

.000

.000

.009

.010

.000

.000

.729

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

CB(bin)

Correl

1.803

a.227

a.268

a-.1

06.000

.699

a.700

a.273

a.179

a-.041

.012

-.073

Sig.

.000

.001

.000

.108

.996

.000

.000

.000

.007

.534

.857

.273

CB(w

)N

229

229

229

229

229

229

229

229

229

229

229

229

229

Correl

1.305

a.307

a-.0

92.038

.442

a.440

a.111

.048

-.034

.009

-.087

Sig.

.000

.000

.164

.565

.000

.000

.094

.472

.608

.889

.189

N229

229

229

229

229

229

229

229

229

229

229

229

CC(bin)

Correl

1.968

a.058

.038

.099

.095

.004

.119

.164

b.294

a-.0

18

Sig.

.000

.384

.562

.135

.153

.952

.073

.013

.000

.788

N229

229

229

229

229

229

229

229

229

229

229

CC(w

)Correl

1.060

.055

.131

b.126

.020

.156

b.160

b.326

a-.0

60

Sig.

.364

.408

.047

.056

.765

.019

.016

.000

.370

N229

229

229

229

229

229

229

229

229

229


Tab

le7

(contin

ued)

POP

REG_P

OP

ACC_Z

ONE

DEG

CB(bin)

CB(w

)CC(bin)

CC(w

)A_S

EC

C_S

EC

ART

DEP T

LDT

UNLDT

CLUST

(bin)

CLUST

(w)

MOD

A_S

EC

Correl

1-.3

44a

-.156

b-.1

56b

-.157

b-.1

37b

.070

.100

-.066

Sig.

.000

.018

.018

.017

.039

.288

.130

.323

N229

229

229

229

229

229

229

229

229

C_S

EC

Correl

1.100

.096

-.059

.035

.076

.078

.127

Sig.

.133

.147

.377

.600

.250

.240

.056

N229

229

229

229

229

229

229

229

ART

Correl

1.999

a.388

a.275

a.031

.095

-.033

Sig.

.000

.000

.000

.646

.152

.617

N229

229

229

229

229

229

229

DEP T

Correl

1.393

a.272

a.028

.090

-.029

Sig.

.000

,000

.670

.174

.668

N229

229

229

229

229

229

LDT

Correl

1.594

a-.0

18.028

-.036

Sig.

.000

.785

.669

.586

N229

229

229

229

229

UNLDT

Correl

1.093

.218

a-.016

Sig.

.162

.001

.813

N229

229

229

229

CLUST

(bin)

Correl

1.791

a-.020

Sig.

.000

.767

N229

229

229

CLUST

(w)

Correl

1-.088

Sig.

.183

N229

229

aCorrelatio

nissignificantatthe0.01

level(2-tailed)

bCorrelationissignificantatthe0.01

level(2-tailed)


Tab

le8

Resultsof

correlationanalysis(variables

calculated

onweightedglobalsets-WGS)

POP

REG_P

OP

ACC_Z

ONE

DEG

CB(bin)

CB(w

)CC(bin)

CC(w

)A_S

EC

C_S

EC

ART

DEP T

LDT

UNLDT

CLUST

(bin)

CLUST

(w)

MOD

POP

Correl

1.123

.030

.235

a.292

a.078

.107

.167

b-.1

56b

.051

.359

a.360

a.406

a.615

a.145

b.216

a-.0

13

Sig.

.063

.650

.000

.000

.240

.106

.012

.018

.441

.000

.000

.000

.000

.028

.001

.845

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

REG_P

OP

Correl

1-.3

69a

.072

.131

b.076

-.043

-.028

-.649

a.272

a.224

a.226

a.194

a.115

-.095

-.100

.100

Sig.

.000

.278

.049

.249

.516

.672

.000

.000

.001

.001

.003

.081

.154

,132

.131

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

ACC_Z

ONE

Correl

1-.0

53-.0

65-.0

35.122

.093

.43a

-.388

a-.0

93-.0

93-.0

10.018

.052

.098

.088

Sig.

.422

.324

.600

.065

.162

.000

.000

.161

.160

.883

.786

.432

.137

.186

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

229

DEG

Correl

1.673

a.633

a.529

a.546

a-.0

84.188

a.608

a.599

a.176

a.164

b.374

a.335

a.223

a

Sig.

.000

.000

.000

.000

.207

.004

.000

.000

.008

.013

.000

.000

.001

N229

229

229

229

229

229

229

229

229

229

229

229

229

229

CB(bin)

Correl

1.804

a.232

a.271

a-.1

07-.0

03.699

a.700

a.272

a.178

a.000

.033

.098

Sig.

,000

.000

.000

.106

.964

.000

.000

.000

.007

.994

.620

.140

N229

229

229

229

229

229

229

229

229

229

229

229

229

CB(w

)Correl

1.310

a.312

a-.0

93.035

.443

a.440

a.110

.046

.028

.035

.131

b

Sig.

.000

.000

.161

.599

.000

.000

.097

.487

.677

.595

.048

N229

229

229

229

229

229

229

229

229

229

229

229

CC(bin)

Correl

1.968

a.058

.031

.100

.096

.006

.119

.407

a.371

a.492

a

Sig.

.000

.379

.641

.130

.148

.928

.073

.000

.000

.000

N229

229

229

229

229

229

229

229

229

229

229

CC(w

)Correl

1.061

.049

.132

b.127

.021

.155

b.398

a.403

a.447

a

Sig.

.359

.461

.046

.055

.751

.019

.000

.000

.000

N229

229

229

229

229

229

229

229

229

229

A_S

EC

Correl

1-.3

44a

-.156b

-.156

b-.1

57b

-.137

b.100

.125

.017

Sig.

.000

.018

.018

.017

.039

.130

.060

.797

N229

229

229

229

229

229

229

229

229


Tab

le8

(contin

ued)

POP

REG_P

OP

ACC_Z

ONE

DEG

CB(bin)

CB(w

)CC(bin)

CC(w

)A_S

EC

C_S

EC

ART

DEP T

LDT

UNLDT

CLUST

(bin)

CLUST

(w)

MOD

C_S

EC

Correl

1.100

.096

-.059

.035

.049

.057

-,043

Sig.

.133

.147

.377

.600

.459

.388

.521

N229

229

229

229

229

229

229

229

ART

Correl

1.999

a.388

a.275

a.071

.110

.069

Sig.

.000

.000

.000

.282

.097

.302

N229

229

229

229

229

229

229

DEP T

Correl

1.393

a.272

a.067

.104

.067

Sig.

.000

.000

.315

.116

.309

N229

229

229

229

229

229

LDT

Correl

1.594

a-.0

02.032

-.016

Sig.

.000

.976

.629

.815

N229

229

229

229

229

UNLDT

Correl

1.131

b.223

a-.0

19

Sig.

.047

.001

.770

N229

229

229

229

CLUST

(bin)

Correl

1.855

a.041

Sig.

.000

.535

N229

229

229

CLUST

(w)

Correl

1.021

Sig.

.755

N229

229

aCorrelatio

nissignificantatthe0.01

level(2-tailed)

bCorrelationissignificantatthe0.01

level(2-tailed)


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