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Existing algorithms that mine graph datasets to discover patterns corresponding to frequently occurring sub-graphs can operate efficiently on graphs that are sparse, contain a large number of relatively small connected components, have vertices with low and bounded degrees, and contain well-labeled vertices and edges. However, for graphs those do not share these characteristics, these algorithms become highly unintelligent. In this paper, we present a novel algorithm conjunction graph-based frequent fast discovering(CGFD) for mining complete frequent itemsets. This algorithm is referred to as the CGFD algorithm from hereon. In this algorithm, we employ the graph-based pruning to produce frequent patterns. Experimental data show that the CGFD algorithm outperforms that algorithm TM.