Link analysis method in general and Hyperlink-Induced Topic Search (HITS) algorithm in particular is used for analyzing graph in many important contexts, including ranking search results based on the hyperlink structure of the World Wide Web and privacy analysis of social networks with the purpose of identifying the role of each object (node) of graph by computing node weight. Similar to almost link analysis algorithms, HITS method consider all edges identically in each computation. However, we find that value of edges in real cases are not identical in analyzing and depend on the relationships/associations in content of two endings. Therefore, in HITS, edge weight should be also computed so that be suitable with value of corresponding relationship/association. Benefiting from the edge weighting, we can treat the problems of "invaluable edges" and their relevant nodes (normally as "rubbishes") in analysis. With this motivation, an improvement HITS (E-HITS) is proposed in this paper. In proposed method, we analyze the meaning of edge, corresponding relationship/association and its characteristics (especially as "group-based") as basis for edge-weight calculation, in which, the calculation is only based on the available hub and authority parameters on graph. Experiments on simulation graphs as well as on real web-graph data show evidently that along with edge weighting, our proposed method can remove the impacts of invaluable edges as well as rubbish nodes in analysis, give the result more positively and objectively than the original HITS method.