We proposed a 3-D protein structure using a simple and connected graph, where nodes indicate amino acids and edges represent contact distances between amino acids. Based on these graph structures, we present a graph mining algorithm to determine the crucial subgraphs in these graphs, which can be applied to classify protein structural families. The proposed algorithm was compared with BLAST, BLAT, and DALI. Moreover, an experiment was conducted, in which characteristic sub-structural patterns were found in several protein families within the Protein Data Bank.