Bayes Inference Of Exponential Degree Distribution Complex Network Model

The core view of modern network science is that the real world complex networks are generally scale free,that is,the node distribution with k degree of network follows the power law,attenuating in the form of k^-?,and generally 2<?<3.Broido and Clauset used power law fitting and rationality test on about 1000 datasets from different fields of society,biology and information in 2019,that the experimental results greatly negate the view of scale free network universality and reveal the diversity of complex network structures in the real world.So it is significant to add new ideas and research mechanism,and explore new network structure to study the real world network law.Actually,the exponential degree distribution complex network is particularly common.The exponential degree distribution has been found in many real world complex networks,and based on this,it is of great significance to accurately identify exponential degree distribution complex networks for understanding and modeling complex systems.However,the existing methods for estimating exponential degree distribution complex network data are not optimal enough.A class uses simple graph methods that consistently produce fluctuating and inaccurate exponential estimates.The other class using truncated MLE proposed by Clauset and Newman and its derivative methods,which lack independence and data utilization,and there is still space for improvement in accuracy.In this paper,we use random graph theory to go back to the development of complex network theory itself,and propose a novel exponential degree distribution complex network parameter estimation method,which is as follows:Firstly,the generalized random graph theory is used to model the complex network with degree distribution follows the exponential,introducing the theory and proving the flow,and capture the derivation process of the parameter of exponential degree distribution network mod-el;After that,involving in the Bayesian process,the captured parameter information is esti- mated by Bayes,studying the posterior distribution of network model parameter,and MCMC numerical simulation is designed to estimate the network model parameter;Then,using the Bayes-MCMC to the simulated network data and real network data,set up MLE control variables experimental group,and observe the estimation effect of the method;Lastly,for the estimation results of the Bayes-MCMC on the real world network data,the Kolmogorov-Smirnov is used to test the goodness of fit of the exponential degree distribution of the network model,and the experimental results are shown.We simulate 9 groups of exponential degree distribution complex networks,using the Bayes-MCMC to estimate the degree distribution parameters of the network model,compared with the truncated MLE proposed by Clauset and Newman,and the conclusion is that the param-eters estimated by Bayes-MCMC are closer to the actual parameters,that show a better estima-tion effect without loss of generality.The exponential distribution network models are obtained by using the Bayes-MCMC on 4 real world network data,and making the Kolmogorov-Smirnov goodness of fit tests between network data and the exponential distribution network models,that tests are carried out successfully,which prove that the proposed method is effective.