Statistical-mechanical iterative algorithms on complex networks

Abstract

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{á}si-Albert's scale-free networks.

7 pages, 6 figures

References in corpus (17)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Finding and evaluating community structure in networks
• Epidemic dynamics and endemic states in complex networks
• Immunization of complex networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Search in Power-Law Networks
• The random K-satisfiability problem: from an analytic solution to an efficient algorithm
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Path finding strategies in scale-free networks
• Performance of networks of artificial neurons: The role of clustering
• Efficient Hopfield pattern recognition on a scale-free neural network
• Potts model on complex networks
• Topology and Computational Performance of Attractor Neural Networks
• Recoverable prevalence in growing scale-free networks and the effective immunization

Cited by in corpus (1)

• Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs