Random field Ising model and community structure in complex networks

Details Random field Ising model and community structure in complex networks Random field Ising model and community structure in complex networks

2005-02-28

arxiv.org/abs/cond-mat/0502672v1

Eur. Phys. J. B 50, 431 (2006)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures

Scientific paper

10.1140/epjb/e2006-00155-4

We propose a method to find out 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 $B_s = +\infty$, $B_{t} = -\infty$, and $B_{i\neq s,t}=0$ 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 to unweighted and weighted networks equally well. We demonstrate the performance of the method by applying it to the Barab\'asi-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network.

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