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The contents of multimedia data has complex relationships including deeply nested whole-part and the many-to-many relationships. This paper proposes a data model incorporating the concepts of directed graphs, recursive graphs, and hypergraphs in order to represent the contents of multimedia data. In the proposed data model, an instance is represented with a directed recursive hypergraph called an instance graph. The logic-based operation called rewrite is introduced. It gives us powerful querying capability because regular expressions on paths can be specified in retrieving instance graphs from collection graphs.