This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted, undirected, graph. It is based on a Markov-chain model of random walk through the database. The suggested quantities, representing dissimilarities (or similarities) between any two elements, have the nice property of decreasing (increasing) when the number of paths connecting those elements increases and when the "length" of any path decreases. The model is evaluated on a collaborative recommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. The model, which nicely fits into the so-called "statistical relational learning" framework as well as the "link analysis" paradigm, could also be used to compute document or word similarities, and, more generally, could be applied to other database or web mining tasks.