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.


Social Network Random Graph Degree Distribution Maximal Clique Social Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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