2009/12/22 by Alicia Miralles, Alícia Miralles, Francesc Comellas +2 · 17 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Average path length #Biological network #Cluster analysis #Clustering coefficient #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Data mining #Degree (music) #Degree distribution #Function (biology) #Gene Regulatory Network Analysis #Graph #Logarithm #Mathematics #Modular design #Path (computing) #Relation (database) #Scale-free network #Shortest path problem #Theoretical computer science #Topological and Geometric Data Analysis #Topology (electrical circuits) #physics.soc-ph
paper · pdf · doi:10.1016/j.physa.2009.12.056
published in Physica A Statistical Mechanics and its Applications 389(9), 1955-1964 (Elsevier BV) · Accepted for publication in Physica A
arxiv created 2009/12/22 · openalex publication_date 2010/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases - usually associated with topological restrictions- their clustering is low and they are almost planar. In this paper we introduce a family of graphs which share all these properties and are defined by two parameters. As their construction is deterministic, we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution, degree correlation, diameter, and average distance, as a function of the two defining parameters. Thus, the graphs are useful to model some complex networks, in particular several families of technological and biological networks, and in the design of new practical communication algorithms in relation to their dynamical processes. They can also help understanding the underlying mechanisms that have produced their particular structure.