Mutual or unrequited love: identifying stable clusters in social networks with uni- and bi-directional links

  • Authors:
  • Yanhua Li;Zhi-Li Zhang;Jie Bao

  • Affiliations:
  • University of Minnesota, Twin Cities;University of Minnesota, Twin Cities;University of Minnesota, Twin Cities

  • Venue:
  • WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
  • Year:
  • 2012

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Abstract

Many social networks, e.g., Slashdot and Twitter, can be represented as directed graphs (digraphs) with two types of links between entities: mutual (bi-directional) and one-way (uni-directional) connections. Social science theories reveal that mutual connections are more stable than one-way connections, and one-way connections exhibit various tendencies to become mutual connections. It is therefore important to take such tendencies into account when performing clustering of social networks with both mutual and one-way connections. In this paper, we utilize the dyadic methods to analyze social networks, and develop a generalized mutuality tendency theory to capture the tendencies of those node pairs which tend to establish mutual connections more frequently than those occur by chance. Using these results, we develop a mutuality-tendency-aware spectral clustering algorithm to identify more stable clusters by maximizing the within-cluster mutuality tendency and minimizing the cross-cluster mutuality tendency. Extensive simulation results on synthetic datasets as well as real online social network datasets such as Slashdot, demonstrate that our proposed mutuality-tendency-aware spectral clustering algorithm extracts more stable social community structures than traditional spectral clustering methods.