2007/08/31 by D. M. Smith, David M. D. Smith, Chiu Fan Lee +2 · 1 citation
Mathematics · Physics and Astronomy · Psychology · #Algorithm #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Degree distribution #Discrete mathematics #Formalism (music) #Graph #Mathematics #Mental Health Research Topics #Opinion Dynamics and Social Influence #Physics #Random graph #Statistical physics #physics.soc-ph
paper · pdf · doi:10.1103/physreve.77.036112
published as Phys. Rev. E 77, 036112 (2008) · This updated version has been expanded to include a number of new results. 19 pages, 11 figures. Minor Typos corrected
arxiv created 2008/02/04 · openalex publication_date 2008/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce the link-space formalism for analyzing network models with degree-degree correlations. The formalism is based on a statistical description of the fraction of links l(i,j) connecting nodes of degrees i and j. To demonstrate its use, we apply the framework to some pedagogical network models, namely, random attachment, Barabási-Albert preferential attachment, and the classical Erdos and Rényi random graph. For these three models the link-space matrix can be solved analytically. We apply the formalism to a simple one-parameter growing network model whose numerical solution exemplifies the effect of degree-degree correlations for the resulting degree distribution. We also employ the formalism to derive the degree distributions of two very simple network decay models, more specifically, that of random link deletion and random node deletion. The formalism allows detailed analysis of the correlations within networks and we also employ it to derive the form of a perfectly nonassortative network for arbitrary degree distribution.