Finding communities in graphs is one of the most well- studied problems in data mining and social-network analysis. In many real applications, the underlying graph does not have a clear community structure. In those cases, selecting a single community turns out to be a fairly ill-posed problem, as the optimization criterion has to make a difficult choice between selecting a tight but small community or a more inclusive but sparser community.

In order to avoid the problem of selecting only a single community we propose discovering a sequence of nested communities. More formally, given a graph and a starting set, our goal is to discover a sequence of communities all containing the starting set, and each community forming a denser subgraph than the next. Discovering an optimal sequence of communities is a complex optimization problem, and hence we divide it into two subproblems: 1) discover the optimal sequence for a fixed order of graph vertices, a subproblem that we can solve efficiently, and 2) find a good order. We employ a simple heuristic for discovering an order and we provide empirical and theoretical evidence that our order is good.


community discovery monotonic segmentation graph mining nested communities 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nikolaj Tatti
    • 1
  • Aristides Gionis
    • 1
  1. 1.Helsinki Institute for Information Technology, Department of Information and Computer ScienceAalto UniversityFinland

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