Detecting the Structure of Social Networks Using (α,β)-Communities

  • Jing He
  • John Hopcroft
  • Hongyu Liang
  • Supasorn Suwajanakorn
  • Liaoruo Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6732)


An (α,β)-community is a subset of vertices C with each vertex in C connected to at least β vertices of C (self-loops counted) and each vertex outside of C connected to at most α vertices of C (α < β) [9]. In this paper, we present a heuristic (α,β)-Community algorithm, which in practice successfully finds (α,β)-communities of a given size. The structure of (α,β)-communities in several large-scale social graphs is explored, and a surprising core structure is discovered by taking the intersection of a group of massively overlapping (α,β)-communities. For large community size k, the (α,β)-communities are well clustered into a small number of disjoint cores, and there are no isolated (α,β)-communities scattered between these densely-clustered cores. The (α,β)-communities from the same group have significant overlap among them, and those from distinct groups have extremely small pairwise resemblance. The number of cores decreases as k increases, and there are no bridges of intermediate (α,β)-communities connecting one core to another. The cores obtained for a smaller k either disappear or merge into the cores obtained for a larger k. Further, similar experiments on random graph models demonstrate that the core structure displayed in various social graphs is due to the underlying social structure of these real-world networks, rather than due to high-degree vertices or a particular degree distribution.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jing He
    • 2
  • John Hopcroft
    • 1
  • Hongyu Liang
    • 2
  • Supasorn Suwajanakorn
    • 1
  • Liaoruo Wang
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthaca
  2. 2.Institute for Theoretical Computer ScienceTsinghua UniversityBeijingChina

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