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Over the years, frequent itemset discovery algorithms have been used to find interesting patterns in various application areas. However, as data mining techniques are being increasingly applied to nontraditional domains, existing frequent pattern discovery approaches cannot be used. This is because the transaction framework that is assumed by these algorithms cannot be used to effectively model the data sets in these domains. An alternate way of modeling the objects in these data sets is to represent them using graphs. Within that model, one way of formulating the frequent pattern discovery problem is that of discovering subgraphs that occur frequently over the entire set of graphs. We present a computationally efficient algorithm, called FSG, for finding all frequent subgraphs in large graph data sets. We experimentally evaluate the performance of FSG using a variety of real and synthetic data sets. Our results show that despite the underlying complexity associated with frequent subgraph discovery, FSG is effective in finding all frequently occurring subgraphs in data sets containing more than 200,000 graph transactions and scales linearly with respect to the size of the data set.