Statistical-mechanical iterative algorithms on complex networks

TL;DR

This paper explores a statistical-mechanical iterative algorithm applied to complex networks, revealing how network heterogeneity influences the algorithm's efficiency, especially in scale-free networks like BA networks.

Contribution

It introduces a heterogeneity-aware iterative algorithm and analyzes its effects on different complex network structures, particularly BA and ER networks.

Findings

Heterogeneity information impacts the algorithm in BA networks.

High-degree nodes facilitate rapid information propagation.

The algorithm's performance varies with network topology.

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{\'a}si-Albert's scale-free networks.