Data Mining and Knowledge Discovery

, Volume 30, Issue 1, pp 99–146 | Cite as

On detecting maximal quasi antagonistic communities in signed graphs

  • Ming Gao
  • Ee-Peng Lim
  • David Lo
  • Philips Kokoh Prasetyo
Article
  • 360 Downloads

Abstract

Many networks can be modeled as signed graphs. These include social networks, and relationships/interactions networks. Detecting sub-structures in such networks helps us understand user behavior, predict links, and recommend products. In this paper, we detect dense sub-structures from a signed graph, called quasi antagonistic communities (QACs). An antagonistic community consists of two groups of users expressing positive relationships within each group but negative relationships across groups. Instead of requiring complete set of negative links across its groups, a QAC allows a small number of inter-group negative links to be missing. We propose an algorithm, Mascot, to find all maximal quasi antagonistic communities (MQACs). Mascot consists of two stages: pruning and enumeration stages. Based on the properties of QAC, we propose four pruning rules to reduce the size of candidate graphs in the pruning stage. We use an enumeration tree to enumerate all strongly connected subgraphs in a top–down fashion in the second stage before they are used to construct MQACs. We have conducted extensive experiments using synthetic signed graphs and two real networks to demonstrate the efficiency and accuracy of the Mascot algorithm. We have also found that detecting MQACs helps us to predict the signs of links.

Keywords

Signed graph Bi-clique Quasi antagonistic community  Enumeration tree Power law distribution 

References

  1. Abello J, Resende MGC, Sudarsky S (2002) Massive quasi-clique detection. In: Latin American theoretical informatics symposium, pp 598–612Google Scholar
  2. Alba RD (1973) A graph-theoretic definition of a socimetric clique. J Math Sociol 3:113–126MATHMathSciNetCrossRefGoogle Scholar
  3. Alvarez-Hamelin I, DallÁsta L, Barrat A, Vespignani A (2008) K-core decomposition of internet graphs: hierarchies, self-similarity and measurement biases. Netw Heterog Media 3(2):371–393MATHMathSciNetCrossRefGoogle Scholar
  4. Anchuri P, Magdon-Ismail M (2012) Communities and balance in signed networks: a spectral approach. In: ASONAM, pp 235–242Google Scholar
  5. Ball B, Karrer B, Newman MEJ (2011) An efficient and principled method for detecting communities in networks. Phys Rev E 84:36103CrossRefGoogle Scholar
  6. Bansal N, Blum A, Chawla S (2004) Correlation clustering. Mach Learn 56(1–3):89–113MATHCrossRefGoogle Scholar
  7. Beyene Y, Faloutsos M, Chau P, Faloutsos C (2008) The ebay graph: How do online auction users interact? In: Computer communications workshops, pp 13–18Google Scholar
  8. Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech 10:1–12Google Scholar
  9. Cartwright D, Harary F (1956) Structure balance: a generalization of Heider’s theory. Psychol Rev 63(5):277–293CrossRefGoogle Scholar
  10. Coen B, Joep K (1973) Algorithm 457: finding all cliques of an undirected graph. Commun ACM 16(9):575–577MATHCrossRefGoogle Scholar
  11. Dandekar P (2010) Analysis and generative model for trust networks. Technique Report, pp 1–5Google Scholar
  12. Donetti L, Mun̈oz MA (2004) Detecting network communities: a new systematic and efficient algorithm. J Stat Mech: P10012(cond-mat/0404652)Google Scholar
  13. Doreian P, Mrvar A (1996) A partitioning approach to structural balance. Soc Netw 18(2):149–168CrossRefGoogle Scholar
  14. Everett M (1982) Graph theoretic blockings, k-plexes and k-cutpoints. J Math Sociol 9:75–84MATHMathSciNetCrossRefGoogle Scholar
  15. Giatsidis C, Thilikos DM, Vazirgiannis M (2011) Evaluating cooperation in communities with the k-core structure. In: 2011 International conference on advances in social networks analysis and mining, pp 87–93Google Scholar
  16. Girvan M, Newman MEJ (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113CrossRefGoogle Scholar
  17. Groshaus M, Szwarcfiter JL (2010) Biclique graphs and biclique matrices. J Graph Theory 63(1):1–16MATHMathSciNetCrossRefGoogle Scholar
  18. Heider F (1946) Attitudes and cognitive organization. J Psychol 21:107–112CrossRefGoogle Scholar
  19. Jamali M, Abolhassani H (2006) Different aspects of social network analysis. In: Web intelligence, pp 66–72Google Scholar
  20. Johnson DS, Yanakakis M, Papadimitriou CH (1988) On generating all maximal independent sets. Inf Process Lett 27(3):119–123MATHCrossRefGoogle Scholar
  21. Karrer B, Newman MEJ (2011) Stochastic blockmodels and community structure in networks. Phys Rev E 83:016107MathSciNetCrossRefGoogle Scholar
  22. Leicht EA, Girvan M, Newman MEJ (2006) Vertex similarity in networks. Phys Rev E 73:026120CrossRefGoogle Scholar
  23. Leskovec J, Huttenlocher DP, Kleinberg JM (2010) Signed networks in social media. In: CHI, pp 1361–1370Google Scholar
  24. Li J, Sim K, Liu G, Wong L (2008) Maximal quasi-bicliques with balanced noise tolerance: concepts and co-clustering applications. In: SIAM international conference on data mining, pp 72–83Google Scholar
  25. Liu G, Wong L (2008) Effective pruning techniques for mining quasi-cliques. In: European conference on machine learning and knowledge discovery in databases, pp 33–49Google Scholar
  26. Liu X, Li J, Wang L (2008) Quasi-bicliques: complexity and binding pairs. In: The 14th annual international computing and combinatorics conference, pp 255–264Google Scholar
  27. Lo D, Surian D, Prasetyo PK, Zhang K, Lim EP (2013) Mining direct antagonistic communities in signed social networks. Inf Process Manag 49(4):773–791CrossRefGoogle Scholar
  28. Lo D, Surian D, Zhang K, Lim EP (2011) Mining direct antagonistic communities in explicit trust networks. In: ACM conference on information and knowledge management, pp 1043–1054Google Scholar
  29. Luce RD (1950) Connectivity and generalized cliques in sociometric group structure. Psychometrika 15:169–190MathSciNetCrossRefGoogle Scholar
  30. Luce RD, Perry AD (1949) A method of matrix analysis of group structure. Psychometrika 14(2):95–116MathSciNetCrossRefGoogle Scholar
  31. Mokken RJ (1979) Cliques, clubs and clans. Qual Quant 13:161–173CrossRefGoogle Scholar
  32. Moon JW, Moser L (1965) On cliques in graphs. Isr J Math 3:23–28MATHMathSciNetCrossRefGoogle Scholar
  33. Mucha PJ, Porter MA (2010) Communities in multislice voting networks. Chaos 20:041108CrossRefGoogle Scholar
  34. Mucha PJ, Richardson T, Macon K, Porter MA, Onnela JP (2010) Community structure in time-dependent, multiscale, and multiplex networks. Science 328:876–878MATHMathSciNetCrossRefGoogle Scholar
  35. Palla G, Derényi I, Farkas I, Vicsek T (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435:814–818CrossRefGoogle Scholar
  36. Palmer CR, Steffan JG (2000) Generating network topologies that obey power laws. In: IEEE globecom 2000, pp 33–37Google Scholar
  37. Ronhovde P, Nussinov Z (2009) Multiresolution community detection for megascale networks by information-based replica correlations. Phys Rev E Stat Nonlinear Soft Matter Phys 80:016,109–19658776CrossRefGoogle Scholar
  38. Sim K, Li J, Gopalkrishnan V, Liu G (2006) Mining maximal quasi-bicliques to co-clustering stocks and financial ratios for value investment. In: IEEE international conference on data mining, pp 1059–1063Google Scholar
  39. Tarjan RE (1972) Depth-first search and linear graph algorithms. SIAM J Comput 1(2):146–160MATHMathSciNetCrossRefGoogle Scholar
  40. Traag VA, Bruggeman J (2009) Community detection in networks with positive and negative links. Phys Rev E 80:036115CrossRefGoogle Scholar
  41. Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  42. Zhang K, Lo D, Lim EP (2010) Mining antagonistic communities from social networks. In: The 14th Pacific-Asia conference on knowledge discovery and data, pp 68–80Google Scholar
  43. Zhang K, Lo D, Lim EP, Prasetyo PK (2013) Mining indirect antagonistic communities from social interactions. Knowl Inf Syst 35(3):553–583CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Ming Gao
    • 1
    • 2
  • Ee-Peng Lim
    • 2
  • David Lo
    • 2
  • Philips Kokoh Prasetyo
    • 2
  1. 1.Institute for Data Science and EngineeringEast China Normal UniversityShanghaiChina
  2. 2.School of Information SystemsSingapore Management UniversitySingaporeSingapore

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