document: A family of dissimilarity measures between nodes generalizing both the shortest-path and the commute-time distances This work introduces a new family of link-based dissimilarity measures between nodes of a weighted directed graph . This measure , called the randomized shortest-path ( RSP ) dissimilarity , depends on a parameter θ and has the interesting property of reducing , on one end , to the standard shortest-path distance when θ is large and , on the other end , to the commute-time ( or resistance ) distance when θ is small ( near zero ) . Intuitively , it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy ( related to θ ) spread in the graph . The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortest-path policy . By adopting a statistical physics approach and computing a sum over all the possible paths ( discrete path integral ) , it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations , where n is the number of nodes . On the other hand , the dissimilarity between every couple of nodes is obtained by inverting an n x n matrix . The proposed measure can be used for various graph mining tasks such as computing betweenness centrality , finding dense communities , etc , as shown in the experimental section .
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