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Summary form only given. Random walks based algorithms give efficient solutions to many distributed problems. The hitting time, i.e. the average time for the walk starting at a given vertex to first hit another given vertex is one of the main quantity used in the analysis of such algorithms. The growing use of peer-to-peer systems leads to a high bandwidth consumption and random walks are currently investigated as a solution to improve peer-to-peer systems efficiency. Such systems are often modeled by weighted graphs. We show how hitting times can be used in peer-to-peer distributed systems to compare the efficiency of deterministic and random-walks based procedures. An expression of the hitting times on a weighted graph in terms of effective resistances is established. Then, an efficient method to compute all the hitting times on a graph is presented. This method is illustrated by a detailed example.