Research On Structure Modeling And Evolution Analysis In Temporal Network

Network is a powerful tool for portraying and analyzing the correlations and interactions between various entities in real system.Temporal network is an extension of the traditional network in the dimension of time,which is a more precisely abstraction of the real complex system.Therefore,the study of temporal network has great theoretical significant and practical value.This article focuses on the key problem of structural modeling and evolution analysis in temporal network,and separately researches the problems of key nodes mining,unknown correlation prediction,and consistent community detection from three levels of network vertices,linkages and communities.Furthermore,we study the common problem of window selection optimization.Mainly includes the following four aspects:First,for mining the important nodes in temporal network,we propose a mathematical representation model named super-evolution matrix for temporal network,and a measurement of the nodes' importance based on the eigenvector centrality of super-evolution matrix.Through defining a super-evolution matrix,we can integrate temporal network snapshots with the inter-layer connections.And the inter-layer relationships between network snapshots can be learned automatically with applying time series analysis method.Besides,due to the special lower triangular format,an iterative and fast calculation method is proposed to solve the eigenvector of the high-dimensional super-evolution matrix.The experimental results show that this method can effectively rank the nodes' importance in temporal network.Second,aiming at the problem of linkage prediction in temporal network,we propose an evolution model of network structure based on time series information,and a hybrid method for predicting unknown linkages with combining the temporal information and structure information.Through introducing univariate and multivariate time series analysis method,we can model the evolution of link frequency between each pair of nodes.Then,combining with the traditional indexes based on network structure similarity we can predict the unknow linkages in temporal network.With taking the two dimensions of time and structure into consideration,the advantages of these two methods are complementary.The experimental results show this method can significantly improve the prediction accuracy in temporal network.Third,for discovering the community structure in temporal network,we propose a model for fusing and optimizing spectral features in temporal network,and a community detection method in temporal network based on the fused spectral feature.Through weighted fusing the Fiedler vectors of normalized Laplacian matrices corresponding to temporal network snapshots,we can cluster the network into different communities based on the fused eigenvector.Therefore,the history community information can be taken into consideration to detect the community at the current moment and avoid the community division bias caused by the fluctuation of network structure.The experimental results show that this method has achieved a better partition quality measured under various evaluation indices of community partition.Forth,aimed at the problem of selecting an appropriate window size in temporal network,we propose two methods to select an appropriate window size based on the network structure distance measures and the temporal network structure features respectively.Selecting an appropriate window size is a common problem in analyzing temporal network,which is also the premise for effectively integrating temporal information.Through designing the network structure distance measures,we can set a threshold and select an appropriate window size depending on its change.And with defining temporal network structure features,we can select an appropriate window size according to time series analysis and AIC criterion.The experimental results show that these methods can effectively select an appropriate window size for temporal network analysis.