Abstract: In order to evaluate network nodes importance effectively, an evaluation method based on efficiency matrix is proposed. Based on node degree and contribution of network node importance comprehensively, the method uses node degree and efficiency matrix to characterize their importance, and to solve deficiency of node's dependence on adjacent nodes only in the method of node importance contribution matrix. Taking actual network sparsity into account,the algorithm has time complexity of O(n²). Finally, feasibility and validity of the algorithm are demonstrated with numerical example analysis. It shows that the method distinguishes node importance differences more directly, simply and effectively. It obtains ideal computing power for large scale complex networks.

Key words: complex networks, efficiency matrix, importance contribution, degree