Researches On The Importance Of Edges Of Complex Networks

In the past forty or fifty years,scholars studying complex networks have begun to study nodes and connected edges in the network from a micro perspective.The research work on edges can be divided into three aspects: the strength of edges,link prediction,and the importance of edges.Edge importance research is different from edge strength measurement and link prediction.Sometimes,the edges with strong connection strength are not very important in the network,and the importance of edges with low connection strength is not necessarily bad;the research object of link prediction is unknown edges in the network,and the importance of edges is right.Study the edges that exist in the network.In detail,the importance of edges is to evaluate the influence of one side in the network.For different types of networks,the significance of edges also differs.For example,in the process of information diffusion,it is often impractical to block all communications of a node.At this time,it is more practical to stop propagation by cutting off some important communication links;for example,it is possible to prevent possible attacks on the power grid by identifying important transmission lines to reduce cascading failures in the power grid.Therefore,it can be concluded that the identification and quantification of important edges in complex networks has important research significance.In recent years,many scholars have made great efforts in researching and discovering the more important edges in the network.However,there are certain problems in these research methods,such as failure to consider the influence of information dissemination factors,and most of the methods are based on the global situation,resulting in high time complexity.Therefore,this article analyzes and discusses the status quo of the importance of the middle of the network from three aspects,and conducts in-depth research based on its existing problems.The innovative results obtained are mainly divided into two aspects:(1)Maintaining the global connectivity of the network is the basic function and role of the edge.This paper starts from the combination structure of graphs and uses the idea of reverse greedy to quantify the importance of connected edges in these networks.The important connected edges in these networks have a great effect on enhancing the robustness of the network.Therefore,in order to obtain a better set of key edges at a reasonable time,a Reverse Greedy Algorithm of Edge(ERG)is proposed:First,reverse selection based on the centrality of the edges connect the edges to minimize the cost function and add them to the initial empty network one by one until you get an edge ordering result that is opposite in importance.Empirical analysis on 9 real network datasets shows that this edge reverse greedy algorithm can measure the importance of edges more accurately than other edge importance measurement methods.(2)In addition to maintaining network connectivity,edge also carries the dissemination of information.Considering that information transmission is susceptible to factors such as the strength of the connection,the role of the sender and recipient,and the way of progagation,while combining the topological properties of the network,this paper proposes an edge importance based on the influence factors of information transmission Measurement method(Information Spreading Model,ISM).By comprehensively considering several factors that affect information spreading and network topology characteristics to characterize the importance of edges,the purpose is to make full use of information from both information transmission and network connectivity to analyze its importance more objectively.Then performance of the ISM algorithm proposed in this chapter on 9 real network data sets.The comparison with the classic edge importance method Jaccard coefficient,bridgeness,betweeness centrality,and reachability index shows that the method is superior to other methods in identifying important edges in the process of network connectivity and diffusion dynamics.In summary,this paper proposes two methods to evaluate the importance of edges based on the shortcomings of edge importance research,and evaluates the performance of the proposed method on real network datasets.The work in this paper provides new research ideas and inspirations for the importance recognition of edges,and has certain significance for maintaining network robustness and rapidly disintegrating networks.