Identifying influential nodes in complex networks is still an open issue. Although various centrality measures have been proposed to address this problem, such as degree, betweenness, and closeness centrality, but most of the current evaluations for node importance in complex networks can not reflect objectively the reality of some real world status. This article based on the Graph Theory, we proposed a new evaluation for finding center and median of graph using the eccentricity of node. In our method, we not only consider the existence of mutual dependence among nodes, but also propose a new algorithm to calculate the eccentricity of node. To evaluate the performance of our method, we used our method to analyze the Advanced Research Project Agency(ARPA) network, which are made to evaluate the feasibility and validity of our method. Next, in order to further verify the accuracy of our method, we simulate cascading failures by continuously removing some important nodes to analyze the network invulnerability.
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