Random field Ising model and community structure in complex networks

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 = +infinity, B-t = -infinity, and B-i not equal s,B-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 Barbasi-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)
Publisher
SPRINGER
Issue Date
2006-04
Language
ENG
Keywords

STATISTICAL-MECHANICS; FINDING COMMUNITIES; METABOLIC NETWORKS; ORGANIZATION; MARKETS

Citation

EUROPEAN PHYSICAL JOURNAL B, v.50, pp.431 - 437

ISSN
1434-6028
DOI
10.1140/epjb/e2006-00155-4
URI
http://hdl.handle.net/10203/2263
Appears in Collection
PH-Journal Papers(저널논문)
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