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Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. We address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a novel graph-theoretic algorithm, called turn-prohibition (TP), that breaks all the cycles in a network and, thus, prevents any interdependence between flows. We prove that the TP-algorithm prohibits the use of at most 1/3 of the total number of turns in a network, for any network topology. Using analysis and simulation, we show that the TP-algorithm significantly outperforms other approaches for breaking cycles, such as the spanning tree and up/down routing algorithms, in terms of network utilization and delay bounds. Our simulation results also show that the network utilization achieved with the TP-algorithm is within a factor of two of the maximum theoretical network utilization, for networks of up to 50 nodes of degree four. Thus, in many practical cases, the restriction of network calculus to feedforward routing networks may not represent a too significant limitation.