Unveiling community structures in weighted networks

Details Unveiling community structures in weighted networks Unveiling community structures in weighted networks

2007-03-07

arxiv.org/abs/physics/0703087v1

Physical Review E 76 (2007) 036101

Physics

Physics and Society

Scientific paper

10.1103/PhysRevE.76.036101

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 $P_{ij}$ 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 graph $G$ has been organized. This topological feature corresponds to the communities in the graph.

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