Reachability queries are of great importance in many research and application areas, including general graph mining, social network analysis and so on. Many approaches have been proposed to compute whether there exists one path from one node to another node in a graph. Most of these approaches focus on static graphs, however in practice dynamic graphs are more common. In this paper, we focus on handling graph reachability queries in dynamic graphs. Specifically we investigate the influence of a given edge in the graph, aiming to study the overall reachability changes in the graph brought by the possible failure/deletion of the edge. To this end, we firstly develop an efficient update algorithm for handling edge deletions. We then define the edge influence concept and put forward a novel computation algorithm to accelerate the computation of edge influence. We evaluate our approach using several real world datasets. The experimental results show that our approach outperforms traditional approaches significantly.