Deterministic small-world communication networks

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. (C) 2000 Elsevier Science B.V. All rights reserved.