An improved belief propagation algorithm for detecting meso-scale structure in complex networks

TL;DR

This paper introduces an improved belief propagation algorithm that enhances detection of meso-scale structures like communities and core-periphery in complex networks, especially dense ones, without increasing computational complexity.

Contribution

The authors propose a novel BP algorithm that overcomes limitations of the original method in dense networks, improving detection accuracy of meso-scale structures.

Findings

Improved BP performs better on dense networks and core-periphery detection.

Both algorithms perform similarly on sparse community detection.

The new algorithm is more stable and accurate in complex network scenarios.

Abstract

The framework of statistical inference has been successfully used to detect the meso-scale structures in complex networks, such as community structure, core-periphery (CP) structure. The main principle is that the stochastic block model (SBM) is used to fit the observed network and the learnt parameters indicate the group assignment, in which the parameters of model are often calculated via an expectation-maximization (EM) algorithm and a belief propagation (BP) algorithm is implemented to calculate the decomposition itself. In the derivation process of the BP algorithm, some approximations were made by omitting the effects of node's neighbors, the approximations do not hold if networks are dense or some nodes holding large degrees. As a result, for example, the BP algorithm cannot well detect CP structure in networks and even yields wrong detection because the nodal degrees in core group are very large. In doing so, we propose an improved BP algorithm to solve the problem in the original BP algorithm without increasing any computational complexity. By comparing the improved BP algorithm with the original BP algorithm on community detection and CP detection, we find that the two algorithms yield the same performance on the community detection when the network is sparse, for the community structure in dense networks or CP structure in networks, our improved BP algorithm is much better and more stable. The improved BP algorithm may help us correctly partition different types of meso-scale structures in networks.