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Characterization and identification of protein complexes in protein-protein interaction (PPI) networks is important in understanding cellular processes. With the core-attachment concept, a novel core-attachment algorithm is proposed by characterizing the protein complex core from the perspective of edges. We reinvite a protein complex core to be a set of closely interrelated edges rather than a set of interrelated proteins. We first identify the edges must belong to a core, and then partition these edges to extract cores. After that, we select the attachments for each complex core to form a protein complex. Finally, we evaluate the performance of our algorithm by applying it on two different yeast PPI networks. The experimental results show that our algorithm outperforms the MCL, CPM, CoAch in terms of number of precisely predicted protein complexes, localization as well as GO semantic similarity. Our proposed method is validated as an effective algorithm in identifying protein complexes and can provide more insights for future biological study. It proves that edge community is a better topological characterization of protein complex.