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In this paper, we propose a graph based algorithm GRG (Graph based method for association Rules Generation) for association rules mining using the frequent closed itemsets groundwork. Association rules mining often base on frequent itemsets which often generates a large number of redundant itemsets that reduce the efficiency. Frequent closed itemsets are subset of frequent itemsets, but they contain all information of frequent itemsets. The most existing methods of frequent closed itemsets mining are apriori-based. The efficiency of those methods is limited to the repeated database scan and the candidate set generation. The new algorithm constructs an association graph to represent the frequent relationship between items, and recursively generates frequent closed itemsets based on that graph. It also constructs a lattice graph of frequent closed itemsets and generates approximate association rules base on lattice graph. It scans the database for only two times, and avoids candidate set generation. GRG shows good performance both in speed and scale up properties.