Finding vital node by node importance evaluation matrix in complex networks

In order to evaluate the node importance in complex network, considering the disadvantages of node deletion method, node contraction method and betweenness method, through defining the node efficiency and the node importance evaluation matrix, a method to find the vital node in complex networks is proposed by using the node importance evaluation matrix. Considered in this method are the node efficiency, node degree and adjacent node importance contributions, and used adjacent node degree and efficiency value to characterize the contribution of their importance. Finally, an optimized algorithm whose time complexity was O(Rn-2) is provided. Experiments show that this method is effective and feasible, and it is applicable to large scale complex networks.