Cayley graphs as models of deterministic small-world networks

摘要

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.