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The framework of statistical inference has been successfully used to detectthe meso-scale structures in complex networks, such as community structure,core-periphery (CP) structure. The main principle is that the stochastic blockmodel (SBM) is used to fit the observed network and the learnt parametersindicate the group assignment, in which the parameters of model are oftencalculated via an expectation-maximization (EM) algorithm and a beliefpropagation (BP) algorithm is implemented to calculate the decompositionitself. In the derivation process of the BP algorithm, some approximations weremade by omitting the effects of node's neighbors, the approximations do nothold 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 andeven yields wrong detection because the nodal degrees in core group are verylarge. In doing so, we propose an improved BP algorithm to solve the problem inthe original BP algorithm without increasing any computational complexity. Bycomparing the improved BP algorithm with the original BP algorithm on communitydetection and CP detection, we find that the two algorithms yield the sameperformance on the community detection when the network is sparse, for thecommunity structure in dense networks or CP structure in networks, our improvedBP algorithm is much better and more stable. The improved BP algorithm may helpus correctly partition different types of meso-scale structures in networks.

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