Motivation: Protein-protein interaction networks are one of the major post-genomic data sources available to molecular biologists. They provide a comprehensive view of the global interaction structure of an organism's proteome, as well as detailed information on specific interactions. Here we suggest a physical model of protein interactions that can be used to extract additional information at an intermediate level: It enables us to identify proteins which share biological interaction motifs, and also to identify potentially missing or spurious interactions. Results: Our new graph model explains observed interactions between proteins by an underlying interaction of complementary binding domains (lock-and-key model). This leads to a novel graph-theoretical algorithm to identify bipartite subgraphs within protein-protein interaction networks where the underlying data are taken from yeast two-hybrid experimental results. By testing on synthetic data, we demonstrate that under certain modelling assumptions, the algorithm will return correct domain information about each protein in the network. Tests on data from various model organisms show that the local and global patterns predicted by the model are indeed found in experimental data. Using functional and protein structure annotations, we show that bipartite subnetworks can be identified that correspond to biologically relevant interaction motifs. Some of these are novel and we discuss an example involving SH3 domains from the Saccharomyces cerevisiae interactome. ?? 2006 Oxford University Press.