Identification Of Key Nodes In Multilayer Networks

Complex network abstracts all kinds of complex and diverse real systems into "graph and network",which is an important tool to understand the world and further solve practical problems.The nodes that can affect the structure and function of the networks to a greater extent are called "key nodes".Identifying the key nodes can effectively control networks with the minimum cost,so accurately mining the key nodes in the network has become an important problem in the network science research.Nowadays,algorithms for mining key nodes are mostly based on single-layer networks with unitary link relations.However,complex systems in the real world are often inextricably linked.For example,the prevalence of an infectious disease is enough to affect transportation,catering,finance and many other fields.This example shows that most networks in the real world need to be studied as a whole,so it is of greater theoretical and practical significance to build multilayer networks model that fits real data.Because of the complex interlayer influence in multilayer networks,the recognition algorithms of key nodes in traditional single-layer networks is no longer applicable to multilayer networks.The main research of this paper includes the construction of multi-layer network model and the identification of key nodes:(1)Aiming at the problems that the existing multilayer networks model cannot accurately describe and analyze the multilayer systems with different number of interlayer nodes,a hyper-interconnected multilayer network model is constructed.This model fully takes into account the heterogeneity of the topological structure between different networks and establishes the inter-layer link according to the interaction between networks.Based on the constructed model,a key node recognition algorithm(Multilayer Biased Walk Rank,MBW-Rank)based on biased walk is proposed.This algorithm defines the importance of each layer based on the topological characteristics and connectivity of the network,and combined with the topological properties of the nodes in the layer as a random walk jump deviation.MBW-Rank can effectively integrate the information of each layer of the network,and at the same time obtain the importance ranking of nodes in each layer and the entire network.Theoretical analysis and experimental comparison verify the accuracy and effectiveness of the method proposed in this paper,indicating that the hyper-interconnected multilayer network model is an accurate description of the system composed of multiple subnetworks with different connection relationships and different numbers of nodes.MBW-Rank can effectively mine the "bridge nodes" that play a key role in the network and provide strategic guidance for the research of multilayer network.(2)Aiming at the problems of ignoring the time dimension and lacking of connection between different time windows in the modeling of temporal networks,which affected the accuracy and scientificity of key node identification,a multilayer temporal network model was constructed.Combined with the multilayer network analysis method,the model completely reveals the structural evolution of time series networks and their dynamic processes over time.Based on the constructed network model,a key node identification algorithm based on biased random walk of node similarity(Multilayer Temporal Biased Page Rank,MTB-PR)was proposed.In this algorithm,the unidirectional influence of adjacent interlayer nodes is proposed according to the time succession,and the influence of adjacent interlayer nodes is distinguished by combining it with the similarity index of interlayer nodes.MTB-PR can obtain the rank of the importance of nodes at different moments and obtain the trajectory of the importance of nodes changing with time,which can effectively mine the key nodes at different moments.In addition,the model and algorithm are applied to the real network in this paper,and the experimental data results show the effectiveness and feasibility of this method.