We propose an algorithm, called Bi-GRAPPIN, to search for similarities across PPI networks. The technique core consists in computing a maximum weight matching of bipartite graphs to compare the neighborhoods of pairs of proteins in different PPI networks. The idea is that proteins belonging to different networks should be matched looking not only at their own sequence similarity, but also at the similarity of proteins they "strongly" interact with, either directly or indirectly. We implemented the method and tested it on both real and synthetic data, showing its effectiveness in solving ambiguous situations and in individuating functionally related proteins. Differently from previous work, the presented algorithm allows to take into account both quantitative and reliability information possibly available about interactions.