Deterministic small-world communication networks

Abstract

Many real life networks, including the World Wide Web, electric power grids, and social networks, are small-world networks. The two distinguishing characteristics of small-world networks are strong local clustering (nodes have many mutual neighbors), and small average distance between two nodes. Small-world networks are promising candidates for communication networks since typical data-flow patterns in communication networks show a large amount of clustering with a small number of “long-distance” communications that need to be completed quickly. Most previous research on small-world networks has used simulations, probabilistic techniques, and random replacements of edges to study the limiting behaviour of these networks. In this paper, we initiate the study of small-world networks as communication networks using graph-theoretic methods to obtain exact results. We construct networks with strong local clustering and small diameter (instead of average distance). Our networks have the additional property that they are regular.