Unveiling community structures in weighted networks.
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.
Alves
Nelson A
NA
Departamento de Física e Matemática, FFCLRP Universidade de São Paulo, Avenida Bandeirantes 3900, CEP 14040-901, Ribeirão Preto, São Paulo, Brazil.
D003198:Computer Simulation; D006801:Humans; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D012944:Social Support