Measuring Node Importance Of Complex Networks Based On Distance

Measuring the importance of nodes is a crucial problem. So far, We have many methods to evaluate nodes’importance such as degree, betweenness, and closeness. These measuring methods have their own characteristics, they can tell the differences between nodes in networks, and find the characters of networks by analysing the nodes of it. However, many existing measures are not able to tell the immediate influence and long-turn influence of a node, and sometimes these methods are not quite persuasive. In this paper, we propose a new measure of node importance based on steps needed to influence a certain percentage of nodes. The importance of a node is related to the distance, or the steps kR, that the node needs to influence R ratio of the network. By using this measuing methods, we can tell the immediate influence and long-turn influence of a node by setting different R, and evaluate a node by its influences in different terms. Moreover, the differential of steps kR2-kR1is also used to measure the node importance. This method has been tested in the sexual relation network of the AIDS. Compared with Degree, betweenness, and closeness, our measure can tell the importance of nodes by the differential of steps, which traditional measures could not. Our findings can provide new insights into the importance of nodes.