An improved belief propagation algorithm for detecting mesoscale structure in complex networks

The framework of statistical inference has been successfully used to detect the mesoscale structures in complex networks such as community structure and core-periphery (CP) structure. The main principle is that the stochastic block model is used to fit the observed network and the learned parameters indicating the group assignment, in which the parameters of model are often calculated via an expectation-maximization 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 the degrees of some nodes are extremely large. As a result, for example, the BP algorithm cannot detect the CP structure in networks and even yields a wrong detection because the nodal degrees in the 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. We find that the original and the improved BP algorithms yield a similar performance regarding the community detection; however, our improved BP algorithm is much better and more stable when the CP structure becomes more dominant. The improved BP algorithm may help us correctly partition different types of mesoscale structures in networks.