Cayley graphs as models of deterministic small-world networks

  • Authors:
  • Wenjun Xiao;Behrooz Parhami

  • Affiliations:
  • Department of Computer Science, South China University of Technology, Guangzhou 510641, P.R. China;Department of Electrical & Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA

  • Venue:
  • Information Processing Letters
  • Year:
  • 2006

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Abstract

Many real networks, including those in social, technological, and biological realms, are small-world networks. The two distinguishing characteristics of small-world networks are high local clustering and small average internode distance. A great deal of previous research on small-world networks has been based on probabilistic methods, with a rather small number of researchers advocating deterministic models. In this paper, we further the study of deterministic small-world networks and show that Cayley graphs may be good models for such networks. Small-world networks based on Cayley graphs possess simple structures and significant adaptability. The Cayley-graph model has pedagogical value and can also be used for designing and analyzing communication and the other real networks.