Bursty Subgraphs in Social Network

1. BurstySubgraphs in Social Network Tam SiuLun, Calvin

2. Subgraphs • Users as the nodes • Connections edges • Become “friends” or follow each others • Like, share, retweet

3. Graph Models • Action graph • Detailed Model of all activities (like, share, become fd, etc) • Holistic graph • Consolidate all actions generated by users • An aggregate view on each user

4. Action graph • Describe topics by a set of keywords Sk • Contact keyword -> relevant • Each nodes (action) is associated with timestamp and user • Link exists between actions • T(a)

5. Holistic graph • Each nodes reprseents a user • Link -> socially connected • Weight wu = (ru, du) • ru : faction of actions of u relevant to a given topic • du : total number of actions of u

6. Intrinsic Burst Model • Based on the graphs • Assign burst state sv (busty B or non-busty N) • Actions are emitted at a higher rate at state • For action graph • The time gap x for each vertex • For holistic graph

7. Intrinsic Burst Model • Target: To maximize • The problem can be simplified to

8. Social Burst Model • Fuzzy burst state Su = SuB / SuN • Su > 1 => Bursty • Objective: To minimize

9. Intrinsic Burst Model • Reduce the problem to Min Cut problem

10. Experimental Result • Apply DIBA and SODA with parameters α and λ • 30 Days of Twitter fire hose • 300~400m tweets per day • 25TB on disk • 5 Most popular topics in June • (1) “Colorado high park fire” • (2) “the grand prix race” • (3) “French Open 2012 tennis final match between RafalNadal and Novak Djokovic” • (4) “Euro 2012” • (5) “Mexico Presidential TV debate on June 10”

11. Evaluation • Apply action/holistic graph to the 5 hot topics • Action Graph • #Vertex (tweets) varies from 10k to 1.1m • Holistic Graph • #users > 27.5m • More than 1.5b edges

12. Results • Action graph • Identify users with what actions at what times are bursty • Holistic graph • Identify busty user

13. Advanced Graph Mining for Community Evaluation in Social Networks and the Web Tam SiuLun, Calvin

14. Objective • Identify the modules and, possibly, their hierarchical organization, by only using the information encoded in the graph topology. • Different metrics/ measurements /methods are used • Hub/authorities • Modularity • Density/Diameter/Link distribution etc.... • Centrality/Betweenness • Clustering coefficient • Structural cohesion

15. Community • Depends heavily on the application domain and the properties of the graph under consideration • A community corresponds to a group of nodes with more intra- cluster edges than inter-clusters edges

16. Community Detection • Specify a quality measure (evaluation measure, objective function) that quantifies the desired properties of communities • Apply algorithmic techniques to assign the nodes of graph into communities, optimizing the objective function • They mostly consider that communities are set of nodes with many edges between them and few connections with nodes of different communities

17. Community Evaluation Measures • Evaluation based on internal connectivity • Evaluation based on external connectivity • Evaluation based on internal and external connectivity • Evaluation based on network model

18. Evaluation on Internal Connectivity • Internal density • Edges inside f(S) = ms • Average degree f(S) = 2ms / ns

19. Evaluation on External Connectivity • Expansion f(S) = cs / ns • Cut ratio • Conductance

20. Evaluation based on both • Maximum out degree fraction • Average out degree fraction

21. Evaluation based on network model • Modularity

22. Graph Clustering algorithm • Hierarchical methods • Modularity Based Methods

23. Hierarchical graph clustering • Clusters form hierarchies • Need for a cluster similarity measure • Single linkage clustering vs. complete linkage • Agglomerative algorithms, clusters are iteratively merged if their similarity is sufficiently high • Hierarchical clustering does not require a preliminary knowledge on the number and size of the clusters • E.g. Dendrogram

24. Modularity based method • Initially introduced as a measure for assessing the strength of Communities • Q = (fraction of edges within communities) –(expected number of edges within communities)

25. Modularity based method

26. Modularity Based Method • Larger modularity Q indicates better communities (more than random intra-cluster density) • The community structure would be better if the number of internal edges exceed the expected number • Modularity value is always smaller than 1 • It can also take negative values • Partitions with large negative modularityExistence of subgraphs with small internal number of edges and large number of inter-community edges

27. Newman-Girvan algorithm • A modularity based algorithm • A divisive algorithm (detect and remove edges that connect vertices of different communities) • Idea: try to identify the edges of the graph that are most between other verticesresponsible for connecting many node pairs • Select and remove edges based to the value of betweenness centrality • Betweennesscentrality: number of shortest paths between every pair of nodes, that pass through an edge

28. Newman-Girvan algorithm • Compute betweenness centrality for all edges in the graph • Find and remove the edge with the highest score • Recalculate betweenness centrality score for the remaining edges • Goto step 2