Research On The Node Importance In Directed-Weighted Complex Network

In the field of complex networks,more and more experts and scholars have paid attention to the research of node importance evaluation.The research has profound theoretical significance and practical value.It helps to identify key nodes and maintain the reliability and survivability of the networks.Currently,there are many research achievements about node importance evaluation at home and abroad.But most of them are based on undirected or unweighted networks,which failed to reflect the real world comprehensively and objectively.In reality,most of the networks belong to directed-weighted complex networks,so we need to establish more applicable indicators and evaluation mechanisms.At present,most of the evaluation indicators tend to focus only on the statistical characteristics of the node itself,ignoring the influence of neighbor nodes or even the whole network nodes.Moreover,some of the works,when examining the interaction between nodes,only consider the impact of distance,which is not comprehensive enough.In response to these problems,the paper makes the following researches:(1)Based on the directed-weighted network model,the paper first defines the cross strength index to characterize the local importance of nodes.Through introducing an adjustable variable,the index not only distinguishes between the in-strength and out-strength of nodes,but also helps to discriminate between nodes whose in-degree is 0.Then,from the perspective of the transmission path,the paper analyzes the importance contribution dependencies among all nodes.Emphatically,in the analysis of the contribution ratio,the paper not only considers the distance factors,but also introduces the number of shortest path factors.Moreover,the paper takes other conditions that also affect the ratio into account.One is that the influence node exerts importance contributions on other nodes.The other is that other nodes exert importance contributions on the node to be evaluated.In view of the above factors,the paper constructs three important contribution matrices.Next,the paper uses analytic hierarchy process to get the multiple contribution matrix,thereby obtaining the total importance contribution values,which can characterize the global importance of nodes.Finally,through combining the local importance and the global importance,we get the final evaluation index.(2)In order to verify the evaluation method proposed,the paper selects three kinds of directed-weighted networks to carry out empirical analysis,including the symmetric network,ARPA network,and Chinese high-speed railway network with 8 verticals and 8 horizontals.The empirical process adopts the removal of nodes,cascading failure simulation experiment and other technical means.It is found that compared with other methods,the method proposed in the paper can distinguish between nodes more effectively.Furthermore,the key nodes and hub cities identified by the method can affect the connectivity of networks more significantly,which further verify the effectiveness and reliability of the method.(3)In recent years,the hypernetworks have sprung up.More and more scholars have begun to pay attention to the research of hypernetworks.Therefore,taking the scientific research cooperation hypernetwork as an example,the paper extends the evaluation method from the directed-weighted networks to the hypernetworks,and studies the importance evaluation of authors.Finally,in the field of Library and information,the paper constructs the hypernetwork including 81 authors and 855 papers to make empirical analysis.The empirical results show that the expanded evaluation index can identify the core authors effectively,which further extends the applicability of the proposed method.