1. Monday, June 01, 2015 Online Social Networks: An Introduction Prensenter: IengFat Lam

2. 2 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

3. Monday, June 01, 2015 What is Online Social Network? 1 What is Social Network What is Online Social Network Why Study Online Social Network

4. 4 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

5. 5 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 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

6. 6 What is Social Networks? (cont.) Network #1 Network #2 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://www.self-insight.com/sna.shtml Bob is an information hub Smaller, tighter Three separate groups Larger, looser More effective individually

7. 7 What is Social Networks? (cont.) 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. 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

8. 8 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 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_networking

9. 9 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) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

10. 10 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? 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://visualrevenue.com/blog/uploaded_images/

11. 11 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.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

12. 12 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.) 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://visualrevenue.com/blog/uploaded_images/

13. Monday, June 01, 2015 Structure of Online Social Network 2 Background The evolution of Structure Structure of Components

14. 14 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 node or 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

15. 15 Background (cont.) 1.We have G contains all nodes v and directed edge (e) 2.We record the time when any node or edge is added to G v t when v added to G t when added to G 3.We also know how the graph looks like for any time t G t is G in time t How much nodes and edges What they are 4.All times are Exact moment 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

16. 16 Background (cont.) The Process: 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

17. 17 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.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

18. 18 Reciprocity ( 相互性 ) of a directed graph Fraction of directed edges such that 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

19. 19 Shows t and 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.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 1: Delay (in days) of reciprocity in Flickr final graph.

20. 20 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 The Evolution of Structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

21. 21 The Evolution of Structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 2: Density of Flickr and Yahoo! 360 time graphs, by week 1 2 3

22. 22 The Evolution of Structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 2: Density of Flickr and Yahoo! 360 time graphs, by week 12 3

23. 23 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

24. 24 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. The Evolution of Structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 3: Fraction of nodes in components of various sizes within Flickr and Yahoo! 360 timegraph, by week.

25. 25 Component size distribution for both datasets follows a power law with exponent -2.74 for the Flickr graph, and -3.60 for Yahoo! 360. The Evolution of Structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 3: Fraction of nodes in components of various sizes within Flickr and Yahoo! 360 timegraph, by week.

26. 26 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

27. 27 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 Structure of Components 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

28. 28 Structure of Components 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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 merge 1 -> 2 : 55.9 times of merge Frequently! Rare…

29. 29 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.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Surprise!

30. 30 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? Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

31. 31 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. Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

32. 32 In a brief: 1.U must be a not-giant component 2.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 groups Group1 C : have more then half of U’s total edges Group2 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

33. 33 Structure of Components (cont.) For example (k = 0.6): 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

34. 34 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

35. 35 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 t is the edge that adds the first twinkle t' is the edge that adds the last twinkle. Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

36. 36 The distribution is sharply decreasing, suggesting that stars are formed rather quickly Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

37. 37 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 4: (B) Age of non-trivial stars in the Flickr final graph.

38. 38 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

39. 39 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

40. 40 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 5: Average and effective diameter of the giant component of Flickr and Yahoo! 360 timegraphs, by week.

41. 41 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 5: Average and effective diameter of the giant component of Flickr and Yahoo! 360 timegraphs, by week.

42. 42 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

43. 43 Discard these degree 1 nodes This suggests that There is a small core inside the giant component of extremely high connectivity Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Average diameterEffective diameter Flickr6.017.61 Flickr (discard)4.455.58 Yahoo! 3608.2610.47 Yahoo! 360 (discard) 6.527.95

44. 44 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

45. 45 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 Structure of Components (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

46. Monday, June 01, 2015 Measurement of Online Social Network 3 Background Analysis of Network Structure

47. 47 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-world have 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

48. 48 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 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://www2.toki.or.id/book/AlgDesignManual/BOOK/BOOK4/NODE159.HTM

49. 49 Background (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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).

50. 50 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 ) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

51. 51 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 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://www.flickr.com

52. 52 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 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://www.livejournal.com

53. 53 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 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://www.orkut.com

54. 54 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 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://www.youtube.com

55. 55 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

56. 56 Analysis of network structure High-level statistics 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References FlickrLiveJournalOrkutYouTube Number of users 1,846,1985,284,4573,072,4411,157,827 Estimated fraction of user population crawled 26.9%95.4%11.3%unknown Dates of crawl Jan 9, 2007Dec 9 - 11, 2006Oct 3 - Nov 11, 2006 Jan 15, 2007 Number of friend links 22,613,98177,402,652223,534,3014,945,382 Average number of friends per user 12.2416.97106.14.29

57. 57 Analysis of network structure (cont.) High-level statistics (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References FlickrLiveJournalOrkutYouTube Fraction of links symmetric 62.0%73.5%100.0%79.1% Number of user groups 103,6487,489,0738,730,85930,087 Average number of groups memberships per user 4.6221.25106.440.25

58. 58 Analysis of network structure (cont.) 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) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

59. 59 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

60. 60 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

61. 61 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

62. 62 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

63. 63 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

64. 64 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

65. 65 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

66. 66 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

67. 67 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

68. 68 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 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.

69. 69 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

70. 70 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

71. 71 Analysis of network structure (cont.) Once we remove 10% of the highest indegree nodes Largest SCC partitions into millions of very small SCCs 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 12: Breakdown of network into SCCs when high-degree nodes are removed, grouped by SCC size.

72. 72 Analysis of network structure (cont.) 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

73. 73 Analysis of network structure (cont.) 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References Figure 13: Average path length among the most well connected nodes. The path length increases sub-logarithmically.

74. Monday, June 01, 2015 Conclusions 4

75. 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

76. Monday, June 01, 2015 References 5

77. 77 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 1.What is Online Social Network 2.Structure of Online Social Network 3.Measurement of Online Social Network 4.Conclusion 5.References

78. 78 Questions? Thank you! 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://www.adrants.com/images/social_networks.jpg

79. 79 Backups