Random field Ising model and community structure in complex networks

S. W. Son, H. Jeong, J. D. Noh

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


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 Bs = +∞, Bt = -∞, and Bi≠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.

Original languageEnglish
Pages (from-to)431-437
Number of pages7
JournalEuropean Physical Journal B
Issue number3
StatePublished - Apr 2006


Dive into the research topics of 'Random field Ising model and community structure in complex networks'. Together they form a unique fingerprint.

Cite this