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The exploitation of parallelism in a message passing platform implies a previous modeling phase of the parallel application as a task graph, which properly reflects its temporal behavior. In this paper, we analyze the classical task graph models of the literature and their drawbacks when modeling message passing programs with an arbitrary task structure. We define a new task graph model called temporal task interaction graph (TTIG) that integrates the classical models used in the literature. The TTIG allows us to explicitly capture the ability of concurrency of adjacent tasks for applications where adjacent tasks can communicate at any point inside them. A mapping strategy is developed from this model, which minimizes the expected execution time by properly exploiting task parallelism. The effectiveness of this approach has been proved in different experimentation scopes for a wide range of message passing applications.