2004/10/25 by Alain Barrat, Romualdo Pastor‐Satorras, Romualdo Pastor-Satorras · 3 citations
Mathematics · Physics and Astronomy · #Cluster analysis #Clustering coefficient #Combinatorics #Complex Network Analysis Techniques #Complex network #Degree (music) #Formalism (music) #Graph #Mathematics #Opinion Dynamics and Social Influence #Physics #Preferential attachment #Scale-free network #Statistical physics #Statistics #Theoretical and Computational Physics #Vertex (graph theory) #Vertex model #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.71.036127
published as Physical Review E 71 (2005) 036127
arxiv created 2004/10/25 · openalex publication_date 2005/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a rate equation approach to compute two vertex correlations in scale-free growing network models based on the preferential attachment mechanism. The formalism, based on previous work of Szabo [Phys. Rev. E. 67, 056102 (2002)] for the clustering spectrum, measuring three vertex correlations, is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k , with an appropriate boundary condition. We study the properties of both two and three vertex correlations for linear preferential attachment models, and also for a model yielding a large clustering coefficient. The expressions obtained are checked by means of extensive numerical simulations. The rate equation proposed can be generalized to more sophisticated growing network models, and also extended to deal with related correlation measures. As an example, we consider the case of a recently proposed model of weighted networks, for which we are able to compute a weighted two vertex correlation function, taking into account the strength of the interactions between connected vertices.