2004/09/06 by Jose C. Nacher, J. C. Nacher, N. Ueda +5
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bioinformatics and Genomic Networks #Complex Network Analysis Techniques #Gene Regulatory Network Analysis #cond-mat.other
paper · pdf · doi:10.1103/physreve.71.036132
published as Phys. Rev. E 71 (2005) 036132 · RevTeX, 5 pages, 4 figures
arxiv created 2004/09/06 · openalex publication_date 2005/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.