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In this paper, we bring the concept of hyperclique pattern in transaction databases into the graph mining and consider the discovery of sets of highly-correlated subgraphs in graph-structured databases. To discover frequent hyperclique patterns in graph databases efficiently, a novel algorithm named HSG is proposed. By considering the generality ordering of subgraphs, HSG employs the depth-first/breadth-first search strategy with powerful pruning techniques based on the upper bound of h-confidence measure. The effectiveness of HSG is assessed through the experiments with real world datasets.