Flexible construction of hierarchical scale-free networks with general exponent

Original · EN

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model which 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) k⁻γ) and power-law scaling of the clustering coefficient C(k) k⁻¹. The major novelties 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 γ> 2, and arbitrarily close to any specified value, being able to reproduce most of the observed hierarchical scale-free topologies. In contrast, previous models can not obtain values of γ> 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 non-biological networks.