As we are in the age of big data, graph data become bigger. A big graph normally has an overwhelming number of edges. Existing metrics of edge centrality are not quite suitable for dealing with such a large graph. A novel metric for measuring the importance of edges in a graph is introduced in this paper. Compared with the other six popular matrices with respect to a number of real-world graphs, the proposed metric is capable of capturing the structural feature of a graph in a scalable way. The comprehensive experiments have demonstrated the performance of the proposed metric. According to this metric, a filtering approach is presented to reduce the visual clutter of a layout in a way that the hidden patterns can be revealed gradually. As evidenced by real-world examples, our approach allows users to explore graphs in real-time with a high level of details in an interactive way in order to gain insight into graph data.