Random field Ising model and community structure in complex networks

S.-W. Son, H. Jeong and J. D. Noh ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 50, issue 3, 431-437

Abstract: We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field B s =+∞, B t =-∞, and B i≠s,t =0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.) Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 89.75.Hc Networks and genealogical trees; 89.65.-s Social and economic systems; 05.10.-a Computational methods in statistical physics and nonlinear dynamics; 05.50.+q Lattice theory and statistics (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2006-00155-4

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