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

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,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

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This research was partially supported by the U.S. Air Force Office of Scientific Research under Grant FA9550-09-1-0675, the National Natural Science Foundation of China under Grant 60553001, and the National Basic Research Program of China under Grant 2007CB807900 and 2007CB807901.

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He, J., Hopcroft, J., Liang, H., Suwajanakorn, S., Wang, L. (2011). Detecting the Structure of Social Networks Using (α,β)-Communities. In: Frieze, A., Horn, P., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2011. Lecture Notes in Computer Science, vol 6732. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21285-7

  • Online ISBN: 978-3-642-21286-4

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