The ample availability and importance of large-scale protein-protein interaction (PPI) data demand a flurry of research efforts to understand cells' organization, processes, and functioning by analyzing these data at the network level. In the bioinformatics and data mining fields, network clustering requires a lot of attraction to discover clusters of interacting proteins. Clustering proteins in a PPI network has been an excellent method for discovering functional modules, disclosing functions of unknown proteins, and other tasks in numerous research over the last decade. In this research, a unique graph mining approach is proposed to detect dense neighborhoods (highly connected regions) in an interaction graph, including protein complexes. Our technique first finds size-3 cliques and then expands these size-3 cliques based on their affinity to produce maximal dense regions. To highlight the efficiency of our suggested strategy, we present experimental results using yeast and human protein interaction data. Our predicted complexes match or overlap much better with the gold standard protein complexes in the CYC-2008 and CORUM benchmark databases than other existing approaches.