Ranking vertices or edges of a network by loops: A new approach

We introduce loop ranking, a new ranking measure based on the detection of closed paths, which can be computed in an efficient way. We analyze it with respect to several ranking measures which have been proposed in the past, and are widely used to capture the relative importance of the vertices in complex networks. We argue that loop ranking is a very appropriate measure to quantify the role of both vertices and edges in the network traffic.