2003/03/21 by Bo Söderberg · 71 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Degree distribution #Discrete mathematics #Giant component #Graph #Mathematics #Random graph #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #Vertex (graph theory) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.015102
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 68(1), 015102 (American Physical Society) · 4 pages, no figures, RevTeX
arxiv created 2003/03/21 · openalex publication_date 2003/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles within a common general formalism, and allows for the analytic calculation of observable graph characteristics. In particular, generating function techniques are used to derive the size distribution of connected components (clusters) as well as the location of the percolation threshold where a giant component appears.