Scale Free Interval Graphs

  • Authors:

  • Naoto Miyoshi;Takeya Shigezumi;Ryuhei Uehara;Osamu Watanabe

  • Affiliations:

  • Tokyo Institute of Technology, Tokyo, Japan 152-8552;Tokyo Institute of Technology, Tokyo, Japan 152-8552;JAIST, Ishikawa, Japan 923-1292;Tokyo Institute of Technology, Tokyo, Japan 152-8552

  • Venue:
  • AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2008

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Abstract

Scale free graphs have attracted attention by their non-uniform structure that can be used as a model for various social and physical networks. In this paper, we propose a natural and simple random model for generating scale free interval graphs. The model generates a set of intervals randomly, which defines a random interval graph. The main advantage of the model is its simpleness. The structure/properties of the generated graphs are analyzable by relatively simple probabilistic and/or combinatorial arguments, which is different from the most of the other models for which we need to approximate the processes by certain differential equations. We indeed show that the distribution of degrees follows power law, and it achieves large cluster coefficient.