Assessing and measuring the importance of nodes in a complex network are of great theoretical and practical significance to improve the robustness of the actual system and to design an efficient system structure. The classical local centrality measures of important nodes only take the number of node neighbors into consideration but ignore the topological relations and interactions among neighbors. Due to the complexity of the algorithm itself, the global centrality measure cannot be applied to the analysis of large-scale complex network. The k-shell decomposition method considers the core node located in the center of the network as the most important node, but it only considers the residual degree and neglects the interaction and topological structure between the node and its neighbors. In order to identify the important nodes efficiently and accurately in the network, this paper proposes a local centrality measurement method based on the topological structure and interaction characteristics of the nodes and their neighbors. On the basis of the k-shell decomposition method, the method we proposed introduces two properties of structure hole and degree centrality, which synthetically considers the nodes and their neighbors’ network location information, topological structure, scale characteristics, and the interaction between different nuclear layers of them. In this paper, selective attacks on four real networks are, respectively, carried out. We make comparative analyses of the averagely descending ratio of network efficiency between our approach and other seven indices. The experimental results show that our approach is valid and feasible.
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