2007/03/07 by Nelson A. Alves, Nelson Augusto Alves
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Graph theory and applications #Topological and Geometric Data Analysis #cond-mat.stat-mech #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1103/physreve.76.036101
published as Physical Review E 76 (2007) 036101
arxiv created 2007/03/07 · openalex publication_date 2007/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective transition matrix Pij to account for the probability of going from vertex i to any vertex j of the original connected graph G. Also, we present an algorithm based on the definition of this effective transition matrix among vertices in the network to extract a topological feature related to the manner by which graph G has been organized. This topological feature corresponds to the communities in the graph.