Bayesian Inference For Cores Decomposition Models Of Undirected Random Graphs

Modeling and inference of complex networks have always been the concern of many scholars.As a graph with some special topological properties,the formation mechanism of network is studied by using random graph theory.Because the classical ER random graph model can not meet the needs of real network research,some scholars have proposed more complex network models,such as generalized random graph model,BA scale-free random graph model,and more classical p₁model,Markov model,p^*model in social network re-search.The main methods of parameter inference for these models are pseudo maximum likelihood estimation?MPLE?,approximate maximum likelihood estimation?AMLE?and Bayesian estimation.The main purpose of this paper is to give an effective Bayesian infer-ence for a new cores decomposition network model,and to explore the model some proper-ties.Firstly,this paper introduces the cores decomposition of undirected graphs and the re-lated definitions of the cores decomposition model.The construction of this model is not limited to the degree information of local nodes,but can capture the global information of the whole network,and then simulate it.Then we present an algorithm for generating ran-dom graphs of cores decomposition models with known parameters.Next is the parameter inference of the model,in order to avoid the difficulty of parameter inference caused by the normalising constant which depend on the parameters in the model,we use a new algorithm based on M-H sampling and ADS algorithm.On the other hand,we verify the robustness of estimators through simulation,and apply the model to small-scale real networks with de-generacy m=3 and m=4 to compare the results of Bayesian estimation and maximum likelihood estimation.The experimental results show that Bayesian estimation is effective method for estimating the cores decomposition model of small-scale networks with low de-generacy.