Statistical-mechanical iterative algorithms on complex networks

Details Statistical-mechanical iterative algorithms on complex networks Statistical-mechanical iterative algorithms on complex networks

2005-07-14

arxiv.org/abs/cond-mat/0507322v2

Phys. Rev. E 72, 046135 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 6 figures

Scientific paper

10.1103/PhysRevE.72.046135

The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in BA networks, but does not influence that in ER networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barab{\'a}si-Albert's scale-free networks.

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