Community Detection And Influential Nodes Identification In Time-varying Networks Based On Stochastic Block Model

Community detection is a key problem in the complex network research,which helps analyzing the network structure and function.It has attracted much attention in recent years.Besides,studying the influential nodes is significant to exploring and analyzing networks and there has been some related achievements.However,many methods of detecting communities or influential nodes are designed only for static networks,which ignore the temporal information and are always not ideal to model the real world data.To solve these problems,our work in this paper are as follows:On one hand,we propose a community detection method for time-varying networks based on the degree-corrected block model.The proposed model introduces a regularization term based on the community membership matrix into the objective function of the degree-corrected block model,which can be considered as a method belonging to evolutionary clustering that is a framework of community detection in evolving networks.We propose a kind of algorithm similar to KL method to solve this model.At the same time,we refer to the network cross-validation approach to model selection,so our method is able to deal with the variety of the number of nodes in time-varying networks and unlike some other dynamic community detection methods,we doesn't assume that the number of communities is a constant.Experiments on real time-varying networks show that our method has a better performance with higher accuracy and lower error rate compared with the classical dynamic stochastic block model and the FacetNet method.On the other hand,we apply the community detection method to identify influential nodes in time-varying networks based on identifying such nodes in the temporal communities which make up the time-varying networks.Firstly,we detect the community structures of all the snapshot networks based on the degree-corrected stochastic block model we proposed.After getting the community structures,we capture the evolution of every community in the time-varying network by the extended Jaccard's Coefficient which is defined to map communities among all the snapshot networks.Lastly,we obtain the initial influential nodes of the dynamic network and aggregate them based on three widely used centrality metrics.Experiments on real world datasets demonstrate that our method can identify influential nodes in dynamic networks accurately,at the same time,we also find some interesting phenomena and conclusions that have been validated in complex network or social science.To conclude,we propose a method to detect commmunities in time-varying networks based on the degreee-corrected block model and apply it to real networks.Besides,we apply the degreee-corrected block model to the identification of time-varying network influential nodes,which is significant to analyzing the networks in the real world.