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In this correspondence, an efficient technique for detecting repeating patterns in a graph is described. For this purpose, the searching capability of evolutionary programming is utilized for discovering patterns that are often repeating in such structural data. The approach adopted in this correspondence is hierarchical in nature. Once a pattern is discovered in a particular level of the hierarchy, the graph is compressed using it, and the substructure discovery algorithm is repeated with the compressed graph. The proposed technique is useful for mining knowledge from databases that can be conveniently represented as graphs. The importance of such an endeavor can hardly be overemphasized, given that substantial portion of data that are generated and collected is either structural in nature or is composed of parts and relations between the parts, which can be naturally represented as graphs. A typical example can be the structure of protein as well as computer-aided design circuits that have a natural graphical representation.