Unveiling community structures in weighted networks

Abstract

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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Cited by in corpus (7)

• Community detection in graphs
• Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics
• A Classification for Community Discovery Methods in Complex Networks
• On fast-slow consensus networks with a dynamic weight
• Detecting groups of similar components in complex networks
• Community detection by resistance distance: automation and benchmark testing
• Detectability threshold in weighted modular networks