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...te this matrix-forest based measure, together with the other introduced quantities, in the experimental section (a precise description of this model can be found in Section 6). 3 Some authors recently considered similarity measures based on random-walk models. For instance, Harel & Koren [28] investigated the possibility of clustering data according to some random-walk related quantities, such as the probability of visiting a node before returning to the starting node. They showed through clustering experiments that their algorithm is able to cluster arbitrary non-convex shapes. White & Smyth [62], independently of our work, investigated the use of the average first-passage time as a similarity measure between nodes. Their purpose was to generalize the random-walk approach of Page, Brin & Winograd [47] by capturing a concept of “relative centrality” of a given node with respect to some other node of interest. More recently, Newman [44] suggested to use a random-walk model in order to compute the “betweenness centrality” of a given node in a graph. Newman counts how often a node is traversed during a random walk between two other nodes (a couple of nodes). Then, this quantity is average...

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...milarity queries were answered through graph isomorphism [3]. More broadly, graphs have been used for modeling biological pathways [4], chemical compounds [5], protein structures [6], social networks =-=[7]-=-, and taxonomies [8, 9]. For example, a metabolic pathway is modeled as a set of reactions, enzymes, and metabolites, and an edge is placed between a reaction and a metabolite (or enzyme) if it partic...

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...tively weighted edges in [12]. The task of link prediction in social networks is described in [19] for the case of positive edges. Distance and similarity in unsigned social networks are described in =-=[26]-=-. These measures are based on shortest-path distances and spectral measures such as PageRank and HITS. Graph kernels are described in [2, 14, 16]. Their application to link prediction and recommendati...

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... ranking of objects in a static graph produced using a specified measure. Notable variations from this theme include approaches that rank objects relative to one or more relevant objects in the graph =-=[55; 114; 105]-=- and methods that rank objects over time in dynamic graphs [89; 88]. Jeh and Widom [55] propose a metric for assessing the similarity of two objects based on the degree to which they link to similar o...

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...ts as probabilities that those edges exist and which can handle illegal paths. In this section we present the weight-based model (WM) which is a simplification of PM. Other models can be derived from =-=[11, 24]-=-. WM is a very intuitive model which is suited well for illustrating issues related to computing c(u, v). WM computes c(u, v) as the sum ∑ p∈PL(u,v) c(p) of the connection strength c(p) of each path p...

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...ork (PPIN) analyses. Based on the observation that biological networks share many properties with Web and social networks (28), ToppNet uses extended versions of three algorithms from White and Smyth =-=(31)-=-—PageRank with Priors, HITS with Priors and K-step Markov—to prioritize disease candidate genes by estimating their relative importance in the PPIN to the disease-related genes. For more details about...

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...rticularly because of its applications to search engines. (e.g. PageRank [5], HITS [13]). Ranking social network actors, on the other hand, is employed for exploring scientific collaboration networks =-=[23]-=-, understanding terrorist networks [16, 23], ranking scientific conferences [19] and mining customer networks for efficient viral marketing [7]. While centrality measures are finding their way into tr...