A New Model for a Scale-Free Hierarchical Structure of Isolated Cliques

  • Takeya Shigezumi
  • Yushi Uno
  • Osamu Watanabe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)


Scale-free networks are usually defined as the ones that have power-law degree distributions. Since many of real world networks such as the World Wide Web, the Internet, citation networks, biological networks, and so on, have this property in common, scale-free networks have attracted interests of researchers so far. They also revealed that such networks have some typical properties such as high cluster coefficient and small diameter as well, and a lot of network models have been proposed to explain them. Recently, some new observations for a real world network are reported [12]. It tries to find a special kind of cliques from a network and introduces observations; 1. the size distributions of cliques show a power-law, 2. the degree distribution of the network after contracting those cliques show a power-law, and 3. by regarding the contracted network as the original, 1 and 2 are observed repeatedly. In this paper, we propose a new network model constructed by a ‘clique expansion’ procedure, to explain these new hierarchical structure of cliques.


scale-free network isolated cliques webgraph web structure modelling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Takeya Shigezumi
    • 1
  • Yushi Uno
    • 2
  • Osamu Watanabe
    • 1
  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Osaka Prefecture UniversitySakaiJapan

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