Parameter Estimation Based On Vertex Bi-degree In Directed Networks

In recent years,with the rapid development of computer technology and Inter-net,all kinds of network data to bring tremendous changes in our lives,but also to the development direction of all walks of life and has a great influence on the operation way.Therefore,it is imperative to study and analyze all kinds of network data.More importantly,the research and analysis results of these data are utilized and applied to real life.Statistical modeling is undoubtedly an important tool for analyzing network data.In particular,the exponential random graph model is used by statisticians and various researchers to broadly fit various network data.Firstly,we introduce the scientific representation and backgrounds of network data,the current status of research and the random graph model of exponential family.Then we give a direct estimation based on vertex pairs in the index of bina-ry weighted directed independent random networks based on the undirected ones;Thirdly,we find the error upper bound of the estimation and maximum likelihood estimation and prove the theory by constructing the approximate inverse matrix of Fisher information array.Finally,the rationality of the model is verified by numer-ical simulation and two actual data.