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Suspicious transaction detection is used to report banking transactions that may be connected with criminal activities. Obviously, perpetrators of criminal acts strive to make the transactions as innocent-looking as possible. Because activities such as money laundering may involve complex organizational schemes, machine learning techniques based on individual transactions analysis may perform poorly when applied to suspicious transaction detection. In this paper, we propose a new machine learning method for mining transaction graphs. The method proposed in this paper builds a model of subgraphs that may contain suspicious transactions. The model used in our method is parametrized using fuzzy numbers which represent parameters of transactions and of the transaction subgraphs to be detected. Because money laundering may involve transferring money through a variable number of accounts the model representing transaction subgraphs is also parametrized with respect to some structural features. In contrast to some other graph mining methods in which graph isomorphisms are used to match data to the model, in our method we perform a fuzzy matching of graph structures.