The Research on Approximating the Real Network Degree Distribution Level Based on DCSBM

Many things in the real world can be simplified as a complex system composed of nodes and the relationships between nodes like a graph. But in real life, the actual graph topology that we can get is usually limited. The traditional stochastic block model (SBM) can build graph networks of different sizes. Since the SBM cannot simulate real network well in degree distribution level, this paper aims to study a degree-corrected stochastic block model called DCSBM. We construct the DCSBM in two ways, the stochastic sequence and genetic algorithm constraint. Based on the DCSBM, the phase transition, which shows the theoretical upper limit of the model's performance, was derived by the belief propagation (BP) algorithm. And we use different graph embedding methods, including NetMF, ProNE and BP algorithm, to make some evaluations. We find the DCSBM approximate real graphs well and the phase transition we infer is correct.