Measurement and Analysis of. Alan Mislove, Massimiliano Marcon,KrishnaP.Gummadi, Peter Druschel, Bobby Bhattacharjee

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1 Measurement and Analysis of Online Social Networks Alan Mislove, Massimiliano Marcon,KrishnaP.Gummadi, Peter Druschel, Bobby Bhattacharjee

2 Background Flickr, YouTube, LiveJournal and Orkut. Rely on an explicit user graph to organize locate and share content as well as contacts. Three main factors, Users, Links and Groups.

3 Motivation Help deliberate attempts of manipulation(efficient algorithms to infer the actual degree of shared interest or the reliability of user). Understand the impact of robustness and security of distributed online social networks to the future internet. Impact on other disciplines(social science, online marketing )

4 Related Work Social network Milgram(6 hops), Small world effect, strong and weak tie. Information network SCC(stronly connected component) Complex network theory Power law networks, Scale-free network, Small-world network.

5 Methodology Crawl the user graphs by accessing the public web interface provided by the sites. Able to access to large data sets from multiple sites. Focus on the large weakly connected component(wcc).

6 Challenges in crawling large graphs Crawling the entire connected component. (Crawling entire connection component is not feasible, and small sample set produced biased sample of nodes.) Using only forward links.(only forward links does not necessarily crawl entire WCC)

7 Figure 1

8 Crawling social networks 1. Flickr Photo sharing site based on a social network. Only allows to query forward links. Among 6,902 sample users, 1,859(26%) being discovered during crawl. BFS to rest 5,043 users, only 250(5%) could reach crawled set and were definitively in the WCC.

9 Explore the social network using the remaining missing nodes as seed, only 11,468 new nodes that were not in the connected component of 1.8 million nodes discovered in the original crawl. Inside it, 44.8% no forward links, 29.3% one link, 5.4% two or three links. 20.3% has four or more. It shows the missing nodes tend to have low degree and connected only to small unreachable clusters from the crawl component. Conclusion: the crawl of the large WCC covers a large fraction of the users who are part of WCC

10 2.LiveJournal. Popular blogging sites. Data set covers 5.3 million user and 72 million links. The fraction not reachable by using only forward links is only 7.64%. And in 404,134 possibly missing users, 49.9% has single forward link, 21% has two or three links. 19.4% has four more.

11 3.Orkut Links undirected and link creation requires consent from the target. 11.3% subset as sample dataset, is likely to be similar to other crawls of similar size. Partial BFS crawls will overestimate the average node degree and underestimate the level of symmetry.

12 4. YouTube Video sharing site includes a social network. Query only in the forward direction. No API for export group information. Group information obtained by screenscraping the HTML page attached to user profile. No way to know the number of absent users.

13 Summary The Flickrand YouTube data sets may not contain some of the nodes in the large WCC, but this fraction is likely to be very small. The LiveJournaldata set covers almost the complete population of LiveJournal, and contains the entire large WCC. The Orkutdata set represents a modest portion of the network, and is subject to the sampling bias resulting from a partial BFS crawl.

14 High-level statistics

15 Analysis of network structure 1. Link symmetry Pages with high indegree tend to be authorities. Symmetry increases the overall connectivity of the network and reduces its diameter Symmetry can also make it harder to identify reputable sources of information just by analyzing the network structure, because reputed sources tend to dilute their importance when pointing back to arbitrary users who link to them.

16 2. Power-law node degrees. All of the networks show behavior consistent with a power-law degree distribution.

17 Tested stability. In and out degree power-law exponents shown to differ significantly.

18 Distruibution of incomming and outgoing links over nodes in the web and Flickr graphs.

19 3. Correlation of indegree and outdegree Node with high outdegree also tend to have high indegree.

20 Outdegree to indegree ratio. Can be explained by the high number of symmetric links.

21 4. Path lengths and diameter. Social networks have significantly shorter average path lengths and diameters.

22 5. Link degree correlations. 5.1 Joint degree distribution. The JDD is approximated by the degree correlation function k nn, and increasing k nn indicates a tendency of higher-degree nodes to connect to other high-degree nodes. A decreasing k nn represent the opposite.

23 Figure 6 The exception on YouTube may due to a few extremely popular users on YouTube. Bump at Orkut curve is likely due to the undersampling of users.

24 5.2 Scale-free behavior Scale-free metric of the networks are shown in the legend of Figure 6. A high scale-free metric means that highdegree nodes tend to connect to other highdegree nodes, while a low scale-free metric means that highdegree nodes tend to connect to low-degree nodes.

25 5.3 Assortativity The scale-free metric is related to the assortativitycoefficient r, which is a measure of the likelihood for nodes to connect to other nodes with similar degrees. The assortativity coefficient ranges between -1 and 1; a high assortativitycoefficient means that nodes tend to connect to nodes of similardegree, while a negative coefficient means that nodes likely connect to nodes with very different degree from their own.

26 Calculate the assortativitycoefficients for each of the networks. Flickr LiveJournal Orkut YouTube Web Internet 0.189

27 6. Densely connected Core. Define a core of a network as any (minimal) set of nodes that satisfies two properties: First, the core must be necessary for the connectivity of the network (i.e., removing the core breaks the remainder of the nodes into many small, disconnected clusters). Second, the core must be strongly connected with a relatively small diameter. Thus, a core is a small group of wellconnected group of nodes that is necessary to keep the remainder of the network connected.

28 Remove increasing numbers of the highest degree nodes and analyze the connectivity of the remaining graph.

29 Path length increase as larger subgraphs of the core generated (progressively including nodes ordered inversely by degree).

30 The graphs studied have a densely connected core comprising of between 1% and 10% of the highest degree nodes.

31 7. Tightly clustered fringe. The clustering coefficient of a node with N neighbors is defined as the number of directed links that exist between the node s N neighbors, divided by the number of possible directed links that could exist between the node s neighbors (N(N 1)). The clustering coefficient of a graph is the average clustering coefficient of all its nodes, and we denote it as C.

32 Table 4 Unusually high clustering coefficient suggests the presence of strong local clustering. People tends to be introduced in by friends.

33 Clustering coefficient Outdegree The clustering coefficient is higher for nodes of low degree. (small world network, scale- free)

34 8. Groups. Group size follows power-law. Present tightly clustered communities of users in the social network.

35 Members of smaller user groups tend to be more clustered than those of large groups.

36 User participation in groups varies with out degrees. Low degree node -> very few communities High degree node -> multiple groups

37 Summary: The degree distributions in social networks follow a power-law, and the power-law coefficients for both in-degree and outdegreeare similar. Social networks appear to be composed of a large number of highly connected clusters consisting of relatively low-degree nodes. The networks each contain a large, densely connected core. (10% nodes with highest degree)

38 Discussion 1. Information dessemination and Search Simple unstructured search algorithms could be designed if the core users were to store some state about other users. ( supernodes )

39 2. Trust If tight core is hacked by malicious users, they will easily skew trust paths.(trust inference algorithms.) Users will not be highly trusted unless they form direct links to other users.(gradually pulled in to the core.)

40 Temporal invariance. Repeated crawl carried out on both Flickr and YoTube on May 2007, and result are still valid. Even though the networks are growing rapidly, their basic structure is not changing significantly.

41 Conclusion Social networks have a much higher fraction of symmetric links and also exhibit much higher levels of local clustering

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