Keywords: 
• 有向加权网络 /
• 节点重要性 /
• 多重影响力矩阵 /
• 最短路径条数

Abstract: In complex networks, the node importance evaluation is of great significance for studying the robustness of network. The existing methods of evaluating the node importance mainly focus on undirected and unweighted networks, which fail to reflect the real scenarios comprehensively and objectively. In this paper, according to the directed and weighted complex network model, by analyzing the local importance of the nodes and the dependencies among all the nodes in the whole network, a new method of evaluating the node importance based on a multiple influence matrix is proposed. Firstly, the method defines the concept of cross strength to characterize the local importance of the nodes. The index not only distinguishes between the in-strength and out-strength of the nodes, but also helps to discriminate the differences in importance among each with an in-degree of 0. In addition, to characterize the global importance of the nodes to be evaluated, we use the total important influence value of all the nodes exerted on the nodes, which makes up the deficiencies of the other evaluation methods which just depend on adjacent nodes. Emphatically, in the analysis of the influence ratio of source node on node to be evaluated, we not only take into account the distance factor between nodes, but also introduce the number of the shortest path factors. In order to make the evaluation algorithm more accurate, according to the number of the shortest paths, we present two perspectives to analyze how other factors affect the influence ratio. One is to evaluate how this source node exerts important influence on the other nodes to be evaluated. The other is to analyze how the other source nodes perform important influence on this node to be evaluated. In view of the above factors, three influence matrices are constructed, including the efficiency matrix, and the other two influence matrices from the perspectives of fixing source nodes and target nodes, respectively. Then, we use analytic hierarchy process to weight the three matrices, thereby obtaining the multiple influence matrix, which makes the global importance evaluation more comprehensive. Finally, the method is applied to typical directed weighted networks. It is found that compared with other methods, our method can effectively distinguish between nodes. Furthermore, we carry out simulation experiments of cascading failure on each method. The simulation results further verify the effectiveness of the proposed method.