title: Flexible construction of hierarchical scale-free networks with general exponent.
abstract: Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidence for hierarchical organization in many real networks has also been reported. Here, we present a hierarchical model that reproduces the main experimental properties observed in real networks: scale-free of degree distribution P (k) [frequency of the nodes that are connected to k other nodes decays as a power law P (k) approximately k(-gamma) ] and power-law scaling of the clustering coefficient C (k) approximately k(-1) . The major points of our model can be summarized as follows. (a) The model generates networks with scale-free distribution for the degree of nodes with general exponent gamma>2 , and arbitrarily close to any specified value, being able to reproduce most of the observed hierarchical scale-free topologies. In contrast, previous models cannot obtain values of gamma>2.58 . (b) Our model has structural flexibility because (i) it can incorporate various types of basic building blocks (e.g., triangles, tetrahedrons, and, in general, fully connected clusters of n nodes) and (ii) it allows a large variety of configurations (i.e., the model can use more than n-1 copies of basic blocks of n nodes). The structural features of our proposed model might lead to a better understanding of architectures of biological and nonbiological networks.
authors.affiliation: Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji 611-0011, Japan.
authors.forename: J C
authors.initials: JC
authors.lastname: Nacher
authors.forename: N
authors.initials: N
authors.lastname: Ueda
authors.forename: M
authors.initials: M
authors.lastname: Kanehisa
authors.forename: T
authors.initials: T
authors.lastname: Akutsu