Random field Ising model and community structure in complex networks |
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Authors: | S-W Son H Jeong J D Noh |
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Institution: | (1) Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea;(2) Department of Physics, Chungnam National University, Daejeon, 305-764, Korea |
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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 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.
(Ising, Potts, etc.) |
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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 |
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