When the amount of information in visualization becomes large enough, users can not perceive all elements at the same time. This problem can be solved by removing parts of the information through the process of Filtering. In this paper, we present a novel method for filtering a graph by measuring the important role property of a node. The basic idea of this approach is to quantify the importance of a node as the degree to which it has direct and indirect relationships with the other nodes in a graph. All the nodes are ranked according to their Node Importance Scores, and those less important nodes and their associated edges are then removed or invisible. In comparison with the rule_based approach, our approach is a structure_based one that makes use of the linkage of nodes rather than their semantics. It can therefore be applied to filter any kinds of connected graphs. The examples and applications provided have demonstrated that our approach can effectively reduce the visual complexi...