monday, june 01, 2015 online social networks: an introduction prensenter: iengfat lam

Tuesday, April 18, 2023

Online Social Networks: An IntroductionPrensenter: IengFat LamPrensenter: IengFat Lam

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Outline

1. What is Online Social Networks [1,2]2. Structure of Online Social Network [2]3. Measurement of Online Social Network [1]4. Conclusions 5. References


What is Online Social Network?

1• What is Social Network• What is Online Social Network• Why Study Online Social Network

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What is Social Networks?

• A Social Structure made of • Nodes – generally individuals or organizations

• Individual actors within the networks• Ties ( 聯繫 ) – specific types of interdependency

• Relationships between actors• Values, Visions, Idea

• Operates on may levels• From families up to the level of nations• Play a critical role on

• Determining the way problems are solved• Organizations are run• The degree to which individuals succeed

1. What is Online Social Network

2. Structure of Online Social Network

3. Measurement of Online Social Network

4. Conclusion

5. References

External Source: http://en.wikipedia.org/wiki/Social_network

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What is Social Networks? (cont.)

• In its simplest form• A map of all of the relevant ties between the nodes.• Often displayed in a social network diagram

• Shared Interest and Trust• Adjacent ( 鄰接 ) users in a social network tend to

• Trust each other• Have common interests

• An Example:• Nodes: Members of a department• Ties: Consults Relationship




4. Conclusion

5. References


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• Network #1

• Network #2




4. Conclusion

5. References

External Source: http://www.self-insight.com/sna.shtml

• Bob is an information hub• Smaller, tighter

• Three separate groups• Larger, looser• More effective individually

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• Analysis of Social Network• Determine a network's usefulness to its

individuals• Examine how organizations interact with each

other• An alternate view

• Relationship is more important than individual• Useful for explaining many real-world phenomena

• About Online Social Network• Difference in structure and measure method.• Existing theories vs New forms of behaviors.




4. Conclusion

5. References


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What is Online Social Networks?

• Online Social Networks is • Social Networks built by Social Network Services

• Primarily web based• Provide a collection of various ways for users to

interact• Run by individual corporations

• Organized around users (not content )

• Provides a powerful means• Sharing, organizing, and finding content and contacts




4. Conclusion

5. References

External Source: http://en.wikipedia.org/wiki/Social_networking

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What is Online Social Networks? (cont.)

• Main Components (user-view)• Users accounts

• Registered possibly though a pseudonym ( 筆名 )• Maintaining social relationships• Finding users with similar interests• Locating contributed content and knowledge

• Links • Real-world acquaintances• Online acquaintances• Business contacts

• Groups• Joined by specific interest• Usually controlled by group’s moderator (or creator)




4. Conclusion

5. References

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• Gained significant popularity• Among the most popular sites on the Web

• MySpace (over 190 million users)• Orkut (over 62 million)• LinkedIn (over 11 million)• LiveJournal (over 5.5 million)

Why Study Online Social Network?




4. Conclusion

5. References

External Source: http://visualrevenue.com/blog/uploaded_images/

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• In the future Internet• Likely to play an important role

• Personal and commercial online interaction• Location and organization of information and

knowledge• Online campaigning and viral marketing

• Impacts in future • Internet Traffic • Robustness and Security

Why Study Online Social Network? (cont.)




4. Conclusion

5. References

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• The successful of flicker, MySpace, YouTube etc.• Social networks have become the subject of numerous

startup companies in their own right.• Use of Social Network to support Web2.0 ideas

• Understanding of the graph structure• Evaluate current systems• Design future online social network based systems• To understand the current impact of online social

networks on the Internet.

• Can Improve our understanding of• Opportunities (is it possible?)• Limitations (accurate, size?)• Threats (potential problems?)with any new ideas.

Why Study Online Social Network? (cont.)




4. Conclusion

5. References

External Source: http://visualrevenue.com/blog/uploaded_images/


Structure of Online Social Network

2• Background • The evolution of Structure• Structure of Components

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Background

• Considers • The evolution ( 發展 ) of structure (over time)• Classifying different components

• Time Graph• Each social network is presented as a directed • Time graph :• Every node : and

Every directed edge :has an associated time stamp and

• Indicating the exact moment when the particular nodeor the edge became part of the graph

• For any time , there is an natural graph that comprises all the nodes and edges that have arrived up until time




4. Conclusion

5. References

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Background (cont.)

1. We have G contains all nodes v and directed edge <u,v> (e)2. We record the time when any node or edge is added to G

• v t when v added to G

• <u,v> t when <u,v> added to G

3. We also know how the graph looks like for any time t• Gt is G in time t• How much nodes and edges• What they are

4. All times are Exact moment




4. Conclusion

5. References

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Background (cont.)

• The Process:1. What is Online Social

Network



4. Conclusion

5. References

G = (V,E)

v1

vt1= 10/29/2007 3:28:56

Gt1= ({v1}, {})

G = (V,E)

v1

v2

vt2= 10/29/2007 4:58:12

Gt2= ({v1,v2}, {})

G = (V,E)

v1v2

<v1,v2>t12= 10/30/2007 12:05:30

Gt12= ({v1,v2}, {<v1,v2>})

New edge

v1 added to G v2 added to G <v1,v2> added to G

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• Datasets• Flickr

Active and popular online photo sharing and social networking community.

• Entire Flickr time graph available• Focus 100 weeks from publicity launched (Feb, 2004)• One million nodes and around eight million directed

edges

• Yahoo! 360• social networking website that is part of the Yahoo!

user network.• 40 weeks worth of data (should be from Jan 2006)• Five million nodes and a around seven million directed

edges

Background (cont.)




4. Conclusion

5. References

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• Reciprocity (相互性 ) of a directed graph• Fraction of directed edges <u, v> such that <v, u> also

exists • When you add someone as a friend, he / she will set you

as friend too.

• Results:• Flickr : 70.2%• Yahoo! 360 : 84%• Friendship edges are highly mutual• Reciprocal edges are formed almost simultaneously

(Figure 1)

• We conclude that• We can pretend that the graph is undirected

The Evolution of Structure




4. Conclusion

5. References

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• Shows <u,v>t and <v,u>t’ in the Flickr graph, the distribution of |t-t’|

• Large part is less then 100 days• Yahoo! 360 is similar

The Evolution of Structure (cont.)




4. Conclusion

5. References

Figure 1: Delay (in days) of reciprocity in Flickr final graph.

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• Density of Online Social Network over time• The ratio of undirected edges to nodes

(Figure 2)

• Three clearly marked stages :• Stage 1 – An initial euphoria ( 興奮 ) among a few

enthusiasts• Stage 2 – Corresponds to a natural dying-out of this

euphoria• Stage 3 – True organic growth more and more people

know about the network

• This phenomenon has not been observed before in real social networks





4. Conclusion

5. References

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4. Conclusion

5. References

Figure 2: Density of Flickr and Yahoo! 360 time graphs, by week

1 2 3

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4. Conclusion

5. References

Figure 2: Density of Flickr and Yahoo! 360 time graphs, by week

1 2 3

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• Fraction of nodes in components (Figure 3)• Top band : giant component

• largest connected• Bottom band : singleton nodes

• no links in the social network at all. • The rest of the bands : middle region

• nodes which exist in small isolated neighborhoods.

• Two particularly interesting properties:• Fraction of three components remain almost constant

once steady state (Stage-3) is reached

• In the middle region, each band of the diagram appears fairly constant.

Component formation and evolution




4. Conclusion

5. References

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• The Flickr social network grew by a factor of over 13x from the period x = 40 to x = 100 in the graph

• Component size distribution for both datasets follows a power law with exponent -2.74 for the Flickr graph, and -3.60 for Yahoo! 360.





4. Conclusion

5. References

Figure 3: Fraction of nodes in components of various sizeswithin Flickr and Yahoo! 360 timegraph, by week.

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• Component size distribution for both datasets follows a power law with exponent -2.74 for the Flickr graph, and -3.60 for Yahoo! 360.





4. Conclusion

5. References

Figure 3: Fraction of nodes in components of various sizeswithin Flickr and Yahoo! 360 timegraph, by week.

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• Structure of the middle region• How do components merge with each another?• Assumption:

• non-giant components would grow organically• i.e. : Size 4 + Size 3 = Size 7

• How component merge in time graph actually?(Table 1)

Structure of Components




4. Conclusion

5. References

MID MID

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• The (i, j)-th entry • number of times a component of size I merges with a

component of size j• Almost all the mass in this table is in the bottom row

and the left column





4. Conclusion

5. References

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4. Conclusion

5. References

Table 1: Sizes of components in Flickr and Yahoo! 360 timegraphs when merging, in 1000’s of nodes

For example:1 -> 1 : 205.1 times of merge1 -> 2 : 55.9 times of merge

Frequently!

Rare…

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• The component merges are of primarily two types:• Singletons merging with the current non-giant components and the

giant component• Non-giant components, including singletons merging with the giant

component

• Surprisingly rare:• Two non-giant components merge to produce another non-giant

component

Structure of Components (cont.)




4. Conclusion

5. References

Surprise!

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• It is natural to speculate that:• Some special node in the non-giant component that serves to “attract” the incoming singleton• If so, it would lead to many middle region stars

• A center of high degree and many low-degree nodes connected to the center

• Are components in the middle region Stars?





4. Conclusion

5. References

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• Definition of a Star• Let be the nodes in a connected component that is not the giant component.• is a star if• Otherwise, let be the set of nodes with degree more than and let

be the set of nodes with degree equal to one• For a parameter we define

to be a star if and • We call C the centers of the star and |T| the twinkles.





4. Conclusion

5. References

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• In a brief:1. U must be a not-giant component2. If U have only 2 nodes, it is a star

(one center node and one twinkle)

3. If U have more than 2 nodes, we divide nodes into two groupsGroup1 C : have more then half of U’s total edgesGroup2 T : have only 1 edge

4. U is star If C only have 1 to 2 nodes, and node number of T divides by node number of (U – C) > k, where k is a value from 0 to 1

5. Then C is center and T is twinkles





4. Conclusion

5. References

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• For example (k = 0.6):1. What is Online Social

Network



4. Conclusion

5. References

MID

Total edge num:2|U| = 2IS Star

MID

C

T

T

Total edge num:2|T| / | U \ C | = 2 / 2 = 1IS Star MID

C

C

Total edge num:3|T| / | U \ C | = 0 / 0 = 0IS NOT Star

C

MID

T

C

Total edge num:3|T| / | U \ C | = 2 / 2 = 1IS Star

T

C

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• Ratio of Middle region was composed of stars:• Flickr final graph: 92.8%

• 69,532 centers and 222,564 twinkles• Yahoo! 360 final graph: 88.7%

• 147,071 centers and 264,971 twinkles• The hypothesis is validated.

• We also define• Non-trivial Star

• if it has more than two nodes • let u be the center of a non-trivial star





4. Conclusion

5. References

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• Distribution of the time lag• Between first twinkle u and the last twinkle u'

to join the star (Figure 4)• The distribution of t'−t (in weeks) where

• <u, v>t is the edge that adds the first twinkle

• <u', v>t' is the edge that adds the last twinkle.





4. Conclusion

5. References

v2

1

v1

v2

1

v1

v3

v4

v5

3

2

4

<v2,v1> First TwinkleIn time t

<v5,v1> Last TwinkleIn time t’

Merged

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• The distribution is sharply decreasing, suggesting that stars are formed rather quickly





4. Conclusion

5. References

Figure 4: (A) Distribution of time lag (in weeks) between the first and last twinkle addition to non-trivial stars in the Flickr final graph.

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• Again, a large fraction of stars are more than 10 weeks old• middle section consists of stars that are formed quickly but

have not been absorbed into the giant component yet





4. Conclusion

5. References

Figure 4: (B) Age of non-trivial stars in the Flickr final graph.

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• Structure of the giant component• We want to know:

How does the diameter of the social network behave as a function of time?

• Measure in average diameter• Defined as the length of the shortest path

between a random pair of nodes.• Compared with

• effective diameter• 90-th percentile 百分位數值 of the shortest

path lengths between all pairs of nodes





4. Conclusion

5. References

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• Diameter as a function of time• High correlation with that of density over time

(Figure 5)• Stage - 1 : Almost Flat• Stage - 2 : edge density drop, diameter reach peak• Stage - 3: edge density increasing, diameter

decreasing





4. Conclusion

5. References

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4. Conclusion

5. References

Figure 5: Average and effective diameter of the giant component of Flickr and Yahoo! 360 timegraphs, by week.

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4. Conclusion

5. References

Figure 5: Average and effective diameter of the giant component of Flickr and Yahoo! 360 timegraphs, by week.

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• Structure of the giant component• We want to know (2) :

• Does the giant component have a reasonably small core of nodes with high connectivity?

• Nodes in the giant component have degree 1• Flickr final graph : 59.7% • Yahoo! 360 final graph : 50.4%• contribute to the increase in diameter values





4. Conclusion

5. References

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• Discard these degree 1 nodes

• This suggests that• There is a small core inside the giant

component of extremely high connectivity





4. Conclusion

5. References

Average diameter Effective diameter

Flickr 6.01 7.61

Flickr (discard) 4.45 5.58

Yahoo! 360 8.26 10.47

Yahoo! 360(discard)

6.52 7.95

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• Structure of the giant component• We want to know (3) :

• Are stars merging into the giant component also responsible for the highly-connected core of the giant component?

• Tracking Merged Star:• We remove all star centers, and both the original

twinkles belonging to that star• Giant component remains extremely well

connected





4. Conclusion

5. References

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• We conclude that:• Stars represent

• The primary form of structure outside the giant component

• But represent only a thin layer of structure at the outside of the giant component





4. Conclusion

5. References

Well Connected

Core

Stars layer


Measurement of Online Social Network

3• Background• Analysis of Network Structure

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Background

• Analysis of the structure of four popular online social networks:• Flickr, YouTube, LiveJournal, and Orkut. • At Large scale, compare to the web.

• Validating • Power-law

The probability that a node has degree k is proportional 成比例 to k−y, for large k and y > 1. y is called the power-law coefficient

• Small-worldhave a small diameter 直徑 and exhibit high clustering

• Scale-free properties Power-law networks, high-degree nodes tend to be connected to other highdegree nodes

• previously observed in offline social networks

• Giving insights to structure




4. Conclusion

5. References

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Background (cont.)

• Study the property of• Weakly connected component (WCC)

• A directed graph• It would be connected by ignoring the direction of

edges. • In user graphs of four sites

• Crawling Challenges• Many graphs can only be crawled by following links

in the forward direction• Using only forward links does not necessarily crawl

an entire WCC




4. Conclusion

5. References

External Source: http://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE159.HTM

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Background (cont.)




4. Conclusion

5. References

Figure 6: Users reached by crawling different link types. If only forward links are used, we can reach only the inner cloud

(shaded cloud); using both forward and reverse links crawls the entire WCC (dashed cloud).

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Background (cont.)

• Crawling social networks• Using automated scripts on a cluster of 58 machines• Social network graphs of

Flickr, LiveJournal, Orkut, and YouTube• Retrieved the list of friends for a user we had not yet

visited , added the retrieved users to the list of users to visit

• Continued until we exhausted the list

• corresponds to a BFS (breadth-first search )




4. Conclusion

5. References

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Background (cont.)

• Flickr• Crawl of large WCC conducted on January 9th, 2007• Over 1.8 million users and 22 million links• Used Flickr’s API to conduct the crawl• Forward links only

(unable to crawl the entire large WCC)• Although not complete, covers a large fraction of the

users who are part of the WCC




4. Conclusion

5. References

External Source: http://www.flickr.com

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Background (cont.)

• LiveJournal• Crawl of large WCC conducted on December 9-11,

2006• Over 5.2 million users and 72 million links• Used LiveJournal’s API to conduct the crawl• both forward and reverse links




4. Conclusion

5. References

External Source: http://www.livejournal.com

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Background (cont.)

• Orkut• Is a “Pure” Social network• Between 3rd and November 11th, 2006• Resort to HTML screen-scraping (no API)• Orkut limits the rate download rate• 11.3% sample of the network are likely to be similar

to other crawls of similar size that are done in the same manner

• Results may not be representative




4. Conclusion

5. References

External Source: http://www.orkut.com

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Background (cont.)

• Youtube• Data obtained on January 15th, 2007• over 1.1 million users and 4.9 million links• Use Youtube’s API• Forword link only• Group information by HTML screen-scrap




4. Conclusion

5. References

External Source: http://www.youtube.com

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Background (cont.)

• Summary of crawling• The Flickr and YouTube data sets may not contain

some of the nodes in the large WCC, • but this fraction is likely to be very small.

• The LiveJournal data set covers almost the complete population of LiveJournal,

• contains the entire large WCC.• Orkut data may have bias.• Youtube , don not know number of accounts




4. Conclusion

5. References

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Analysis of network structure

• High-level statistics1. What is Online Social

Network



4. Conclusion

5. References

Flickr LiveJournal Orkut YouTube

Number of users

1,846,198 5,284,457 3,072,441 1,157,827

Estimated fraction of user population crawled

26.9% 95.4% 11.3% unknown

Dates of crawl

Jan 9, 2007 Dec 9 - 11, 2006 Oct 3 - Nov 11, 2006

Jan 15, 2007

Number of friend links

22,613,981 77,402,652 223,534,301 4,945,382

Average number of friends per user

12.24 16.97 106.1 4.29

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Analysis of network structure (cont.)

• High-level statistics (cont.)1. What is Online Social

Network



4. Conclusion

5. References

Flickr LiveJournal Orkut YouTube

Fraction of links symmetric

62.0% 73.5% 100.0% 79.1%

Number of user groups

103,648 7,489,073 8,730,859 30,087

Average number of groups memberships per user

4.62 21.25 106.44 0.25

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• Link symmetry• All three social networks with directed links

(Flickr, LiveJournal, and YouTube) have a significant degree of symmetry

• consistent with that of offline social networks

• Power-law node degrees• The degree distributions of many complex networks,

including offline social networks, have been shown to conform to powerlaws

• Outdegree and indegree complementary互補性 (Figure 7)




4. Conclusion

5. References

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4. Conclusion

5. References

Figure 7: Log-log plot of outdegree (top) and indegree (bottom) complementary cumulative distribution functions (CCDF). All social

networks show properties consistent with power-law networks.

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4. Conclusion

5. References

Figure 7: Log-log plot of outdegree (top) and indegree (bottom) complementary cumulative distribution functions (CCDF). All social

networks show properties consistent with power-law networks.

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• Power-law node degrees (cont.)• All of the networks show behavior consistent with a

power-law network

• Distribution of links across nodes (Figure 8)• In / out link degree distribution • Each of our social networks are very similar• Implies that in the distribution of outgoing links is

similar to that of incoming links• In the Web, incoming links are significantly more

concentrated




4. Conclusion

5. References

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4. Conclusion

5. References

Figure 8: Plot of the distribution of links across nodes. Social networks show similar distributions for outgoing and incoming links, whereas

the Web links shows different distributions.

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• Correlation of indegree and outdegree• For each network, the top 1% of nodes ranked by

indegree has a more than 65% overlap with the top 1% of nodes ranked by outdegree. (Figure 9)

• Active users in social networks also tend to be popular




4. Conclusion

5. References

64





4. Conclusion

5. References

Figure 9: Plot of the overlap between top x% of nodes ranked by outdegree and indegree. The high-indegree and high-outdegree nodes

are often the same in social networks, but not in the Web.

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• Indegree and outdegree of individual nodes • Remarkable correspondence between indegree and

outdegree for all networks (Figure 10)• Over 50% of nodes have an indegree within 20% of

their outdegree (0.2 - 0.8 have ratio of 1)• Can be explained by the high number of symmetric

links




4. Conclusion

5. References

66





4. Conclusion

5. References

Figure 10: CDF of outdegree to indegree ratio. Social networks show much stronger correlation between indegree and outdegree than the Web.

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• Joint degree distribution• Provides insights into the structural properties of

networks

• High-degree node tend to connect to • High or low degree node? (Figure 11)

• The increasing knn (k-th nearest neighbor )• The trend for high-degree nodes to connect to other

high degree nodes can be observed• Scale -Free • except YouTube, caused by celebrity nature




4. Conclusion

5. References

68





4. Conclusion

5. References

Figure 11: Log-log plot of the outdegree versus the average indegree of friends. The scale-free metrics, included in the legend, suggest the

presence of a well-connected core.

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• Scale-free behavior• Value calculated directly from the joint degree

distribution• Ranges between 0 and 1, and measures the extent to

which the graph has a hub-like core• All of the networks with the exception of YouTube show a

significant s• High degree tend to connect high degree• Low degree tend to connect low degree




4. Conclusion

5. References

70


• Densely connected core• Define a core of a network as any (minimal) set of

nodes that satisfies two properties:1. Core must be necessary for the connectivity of the

network 2. The core must be strongly connected with a

relatively small diameter• Remove increasing numbers of the highest degree

nodes • Analyze the connectivity of the remaining graph

• Calculate the size of the largest remaining SCC• The largest set of user who can mutually reach each

other• Figure 12




4. Conclusion

5. References

71


• Once we remove 10% of the highest indegree nodes• Largest SCC partitions into millions of very small SCCs




4. Conclusion

5. References

Figure 12: Breakdown of network into SCCs when high-degree nodes are removed, grouped by SCC size.

72


• Path lengths of subgraphs containing only the highest-degree nodes

• How much the network core contributes towards the small path lengths ? (Figure 13)

• The average path length increases sub-logarithmically with the size of the core

• Overall average path length is 5.67, of which 3.5 hops involve the 10% of nodes in the core with the highest degrees

• High-degree core nodes within roughly four hops of each other

• Densely connected core comprising of between 1% and 10% of the highest degree nodes




4. Conclusion

5. References

73





4. Conclusion

5. References

Figure 13: Average path length among the most well connectednodes. The path length increases sub-logarithmically.


Conclusions

4

75

Conclusions

• Online Social Networks• Have characistics observed in offline social

networks• Power-law• Small-world• Scale-free properties

• High-density core with low-degree Star as outer layer

• In both Large scale snap-shot or time-based evolution




4. Conclusion

5. References


References

5

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References

1. A. Mislove, M. Marcon, K. P. Gummadi, P. Druschel, S. Bhattacharjee. “Measurement and Analysis of Online Social Networks”, Internet Measurement Conference (IMC) 2007.

2. Ravi Kumar, Jasmine Novak, Andrew Tomkins. “Structure and Evolution of Online Social Networks”, Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining KDD '06




4. Conclusion

5. References

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• Questions?

Thank you!




4. Conclusion

5. References

External Source: http://www.adrants.com/images/social_networks.jpg

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monday, june 01, 2015 online social networks: an introduction prensenter: iengfat lam

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