CUT: Community Update and Tracking in Dynamic Social Networks

1. CUT: Community Update and Tracking in Dynamic Social Networks Hao-Shang Ma and Jen-Wei Huang Knowledge and Information Discovery Lab, Dept. of Electrical Engineering, National Cheng Kung University The 7th Workshop on Social Network Mining and Analysis (SNA-KDD'13) joint with the 19th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD'13)

2. About Me • Jen-Wei Huang (黃仁暐) • Knowledge and Information Discovery Lab • Dept. of Electrical Engineering, National Cheng Kung University • Email: jwhuang @ mail.ncku.edu.tw • http://kid.ee.ncku.edu.tw KID Lab, National Cheng Kung University

3. Research • Data Mining and Database • Time Series Mining • Social Network Analysis • Multimedia Information Retrieval • Ubiquitous Computing • Mobile Computing • Cloud Computing • Bioinformatics KID Lab, National Cheng Kung University

4. Outline • Introduction • CUT Algorithm • Experiments • Conclusions • References KID Lab, National Cheng Kung University

5. Introduction • Social networking websites allow users to establish their own personal communities or social networks based on relationships of friends. http://www.facebook.com/ http://twitter.com/ KID Lab, National Cheng Kung University

6. Introduction • Based on the relationships between users, social networks exhibit a community structure. KID Lab, National Cheng Kung University

7. Introduction • The detection of communities in a network usually puts network nodes into groups in such a way that nodes in the same group are densely connected to one another. • An objective function is chosen to determine the quality of a community. • Modularity [1] is a measure of the quality of a partition in terms of the number of intra-community and inter-community edges. KID Lab, National Cheng Kung University

8. Introduction • Social networks are always changing with the time. • We want to quickly and efficiently identify the community structures of a network at every timestamp. • Updating the network structureby tracking previously known information instead of recalculating the relationships of all nodes and edges in the networks. KID Lab, National Cheng Kung University

9. Introduction • In this work, we define the seed of community, which is a collection of 3-cliques where any two of 3-cliques share more than one edge. • By tracking seed of communities, we are able to efficiently update and track the dynamics of communities in a social network. KID Lab, National Cheng Kung University

10. Example Network and 3-clique KID Lab, National Cheng Kung University

11. CUT Algorithm • We propose CUT algorithm, standing for Community Update and Tracking algorithm, to update and track seed of communities. • There are two phases in CUT algorithm. • Initial phase, executed only once. • Find seed of communities • Extend seed of communities to communities • Update and Tracking phase • Maintain and update CAB graph KID Lab, National Cheng Kung University

12. Find Seed of Communities • 1. Find all 3-cliques in a network • 2. Build CBA (Clique Bipartite Adjacent) graph • 3. Determine the seed of communities in a network KID Lab, National Cheng Kung University

13. Find All 3-cliques • Backtracking algorithm KID Lab, National Cheng Kung University

14. All 3-cliques in the Network KID Lab, National Cheng Kung University

15. Clique Adjacent Bipartite Graph KID Lab, National Cheng Kung University

16. All 3-cliques in CAB KID Lab, National Cheng Kung University

17. Determine Seed of Community • DFS-like algorithm to find connected component KID Lab, National Cheng Kung University

18. CAB Graph • The complexity of tracking CAB is lower than that of tracking the original graph • Complexity of building CAB is O(3|C|)=O(|C|) • Complexity of determining the connected component is O(3|C|)=O(|C|) • Easy to combine or split the seeds of community KID Lab, National Cheng Kung University

19. Extend to Communities • Ignore the sparse nodes whose degree is smaller than 2. • Assign the remain nodes to the closest seed of community • Closest: the seed of community which has the most links to the node KID Lab, National Cheng Kung University

20. Update and Tracking Phase • Maintain and Update CAB Graph • If there are some changes in the network, do the following cases • Case 1: New nodes & new edges are added • Case 2: Old nodes & edges are removed • Extend to Communities KID Lab, National Cheng Kung University

21. Case 1: Merge and Join New Node : 20,21 New Edge : (2,8) (5,20), (9,20), (11,21) New 3-cliques: (2,6,8) and (5,9,20) KID Lab, National Cheng Kung University

22. Case 1: Merge and Join • =(), =() • If any two edges link to different seeds of communities, SiandSj, we merge(Si, Sj) • Else if any edge of Ck links to any Si then we Join(Si, Ck) • Complexity is O(3*| new C |) = O(| new C |) KID Lab, National Cheng Kung University

23. Case 2: Split and Removal • If there are nodes removed , we find all edges which connect to the removed nodes N10 is removed. Therefore, (4,10),(6,10) (8,10),(10,12) (10,11) are removed. KID Lab, National Cheng Kung University

24. Node Removed Case - Split • Remove corresponding edges and cliques • Run FindSeedofCommunity algorithm again to update to new seeds of communities • Complexity is O(3|C|+| removed C |) KID Lab, National Cheng Kung University

25. Joint Case There are new nodes added and edges removed at the same time KID Lab, National Cheng Kung University

26. Joint Case • We simply deal with the Case 1 first, and then deal with the Case 2 so that we can decrease the unnecessary splits. • Finally, extend seed of communities to communities. KID Lab, National Cheng Kung University

27. Related Works - Update the Community Structure • Nam P. Nguyen et al. propose a QCA algorithm. [9] • The QCA algorithm uses the already known community structure, and deal with the changing cases, new nodes, new edges, nodes removed, and edges removed based on modularity. • In QCA algorithm, they keep the whole community structure at each timestamp. • Using original CPM in removed case every time, which cost lots of time. • They have to identifying the nodes or edges belong to which type of cases. It costs much time as well. KID Lab, National Cheng Kung University

28. Experiments • Coauthor network (2002~2010) • 1. About 20000 authors in one network • 2. Densely connected graph • 3. Five years as a time period, t1 is 2002-2006 (first update) • 4. Variations of network at each time stamp are small KID Lab, National Cheng Kung University

29. Experiments KID Lab, National Cheng Kung University

30. Experiments • p2p-Gnutella network • 1. t1-t4 is a snapshot from August 4 to 7 2002, about 6000 nodes • 2. Sparse connected graph • 3. Variations of network at each time stamp are large. KID Lab, National Cheng Kung University

31. Experiments KID Lab, National Cheng Kung University

32. Conclusions • We design CUT algorithm for updating community structures in dynamic social networks instead of recalculating relationships of all nodes and edges in the social network. • Keeping seeds of communities in the memory at each timestamp is more efficient than keeping all communities. • Using Clique Adjacent Bipartite graph to update and track seeds of community leads to lower complexity. KID Lab, National Cheng Kung University

33. References • M. E. J. Newman and M. Girvan, “Finding and evaluating community structure in networks,” Phy. Rev. E 69, 2004. • Bowen Yan and Steve Gregory,” Detecting Communities in Networks by Merging Cliques,” ICIS, 2009. • CLAUSET, G., NEWMAN, M. E. and MOORE, C., “Finding community structure in very large networks,” Phys. Rev. E 70, 066111, 2004. • Zhengzhang Chen, Kevin A. Wilson, Ye Jin, William Hendrix and Nagiza F. Samatova, “Detecting and Tracking Community Dynamics in Evolutionary Networks,” ICDMW, 2010. KID Lab, National Cheng Kung University

34. References • Yi Wang, Bin Wu, and Xin Pei, “CommTracker: A Core-Based Algorithm of Tracking Community Evolution,” ADMA, 2008. • Nam P. Nguyen, Thang N. Dinh, Ying Xuan, and My T. Thai. “Adaptive Algorithms for Detecting Community Structure in Dynamic Social Networks,” INFOCOM, 2011. • Vincent D Blondel, Jean-Loup Guillaume, Renaud Lambiotte and Etienne Lefebvre,”Fastunfolding of communities in large networks,” JSTAT, 2008. • Nan Du, Bin Wu, Xin Pei, BaiWang and LiutongXu,” Community Detection in Large-Scale Social Networks,” SNA-KDD, 2007. KID Lab, National Cheng Kung University