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Random field Ising model and community structure in complex networks

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  • S.-W. Son
  • H. Jeong
  • J. D. Noh

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

Suggested Citation

  • S.-W. Son & H. Jeong & J. D. Noh, 2006. "Random field Ising model and community structure in complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(3), pages 431-437, April.
    • Handle: RePEc:spr:eurphb:v:50:y:2006:i:3:p:431-437
    DOI: 10.1140/epjb/e2006-00155-4
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    Cited by:

    1. Liu, Dong & Liu, Xiao & Wang, Wenjun & Bai, Hongyu, 2014. "Semi-supervised community detection based on discrete potential theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 173-182.

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