Deterministic hierarchical networks

Abstract

Recently it has been shown that many networks associated with complex systems are small-world (they have both a large local clustering and a small diameter) and they are also scale-free (the degrees are distributed according to a power-law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems which are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the systems modeled. In this paper we find the radius, diameter, clustering and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks which has been considered for modeling real life complex systems. Moreover a routing algorithm is proposed.