Research On Modeling And Identification Of Important Nodes Of Multilayer Temporal Networks

The identification of important nodes in complex networks is one of the important research contents in network science.Revealing the key nodes in networks has important theoretical and practical significance for understanding the structure and behavior of networks.Key nodes have a greater impact on the topology structure and function of the networks compared with other nodes in complex networks.With the development of science and technology,many complex systems in the real world is no longer isolated,but widely related and interdependent.At the same time,the structure of the systems change dynamically with time.For this kind of complex network system with multi-layer and dynamic characteristics,the traditional networks model can not describe such systems reasonably and effectively.In order to overcome the shortcomings of traditional network models,scholars have proposed multi-layer temporal network to describe complex system with multi-layer and temporal characteristics.In particular,some complex network systems may only contain multi-layer or temporal feature,at this time,multilayer temporal networks will reduce to multi-layer networks or temporal networks.Therefore,multilayer and temporal networks can be regarded as two kinds of special multilayer temporal networks.The research on multilayer temporal network is considered to be the second revolution in the field of complex network,and it is also listed as one of the “ten problems of complex network science”.Furthermore,identifying important nodes in complex network is of practical significance to find the important pathogenic genes,to suppress the spread of the epidemic,to accurately launch advertisements and so on.This paper focuses on the research on modeling and identification of important nodes of multilayer,temporal and multi-layer temporal networks,and applies the importance of nodes to the link prediction in temporal networks.Specifically,the main research contents of this paper are as follows:1.A new ranking method based on topological biased random walk centrality is proposed for identifying the important nodes in multilayer networks.We first establish a multilayer network model with connected edges between different layers to describe multilayer networks,which can be represented by a fourth-order tensor.Then,two transition probability tensors are constructed by introducing topological biased random walk into multi-layer networks.Based on the constructed transition probability tensors,a set of tensor equations is established to define the centrality vectors of nodes and layers in multi-layer networks.Furthermore,in order to obtain the centrality vectors of nodes and layers,a fixed point iterative algorithm that similar to high-order power method is proposed to solve the proposed tensor equations.Under some conditions,the existence and uniqueness of tensor equations and the convergence of iterative algorithm are proved by using Brouwer fixed point theorem.Finally,numerical experiments on a synthetic and two real multi-layer networks to demonstrate the proposed centrality can better identify nodes with strong propagation ability in multilayer network.2.A new f-Page Rank centrality is proposed for identifying the important nodes in temporal networks,which can be regarded as the generalization of Page Rank.We first establish a novel network model to describe the temporal network.In the proposed model,we consider the interaction between different time layer networks(or called snapshots),and the interaction between different snapshots should follow the time order,that is,the future snapshots cannot affect the historical snapshots.In addition,the fourthorder tensor is used to represent the basic structure of temporal networks.Based on the tensor representation of temporal networks,a set of tensor equations with parameters is established to define the centrality vectors of nodes and snapshots in temporal networks.Under some suitable conditions,the existence and uniqueness theorems of f-Page Rank centrality are established.Moreover,in order to obtain the solution of tensor equations,the tensor equations can be solved by developing a fixed point iterative algorithm,of which the convergence can be strictly proved.Finally,numerical experiments on a artificial and two real-world temporal networks(i.e.,Email-Eu-Core and Collegemsg networks)show that f-Page Rank centrality can reasonably and effectively measure the importance of nodes and snapshots.3.MT-HITS(Multilayer temporal HITS)centrality based on the inter-layer similarity is proposed for ranking the nodes in multilayer temporal networks,which defines the authority and hub centrality vectors of nodes.Firstly,based on the multi-layer and temporal network models respectively constructed in Chapter 3 and Chapter 4,a novel multi-layer temporal network model is established.The proposed network model considers not only the interactions between different network layers in each snapshot,but also the interactions between different snapshots,and the interactions between different snapshots should follow time order.In addition,the sixth-order tensor is used to represent the basic structure of the multilayer temporal network.Based on the sixth-order tensor representation of networks,the HITS centrality in single-layer networks is extended to multi-layer temporal networks by establishing a set of tensor equations with parameters,which defines the hub and authority centrality vectors of nodes,layers and snapshots(or called time stamps)in multilayer temporal networks.Under some suitable conditions,the existence and uniqueness theorems of solutions for tensor equations are strictly proved.Moreover,the tensor equations can be solved by developing a fixed point iterative algorithm,of which the convergence and convergence rate can be strictly proved.Finally,the numerical results show that the MT-HITS centrality measure has strong resolution of important nodes.4.The application of node importance in temporal link prediction is studied and a novel temporal link prediction algorithm based on the Page Rank centrality and asymmetric link clustering information is developed,referred to as the GNMFCA(Graph regularized nonnegative matrix factorization based on centrality and asymmetric link).Specifically,we use graph regularization to capture the local information of each slice in temporal networks.While we utilize Page Rank centrality to compute the importance of nodes in each slice,which captures the global information of each slice in temporal networks.Then,by jointly optimizing them in nonnegative matrix factorization model,the proposed model can preserve both the local and global information of each slice in temporal networks simultaneously.Besides,we propose an effective multiplicative updating rules to solve the proposed model and provide theoretical analysis of the proposed iterative algorithm.Finally,numerical experiments on eight artificial and four real-world temporal networks are performed to demonstrate that the prediction accuracy of GNMFCA is higher than some existing prediction algorithms.