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An information theoretic upper bound on the information flow in discrete memoryless networks is found. The networks considered here can have multiple information sources and multiple sinks corresponding to each of the sources (which is also called as multicast). In the special case of networks with a single information source with multiple sinks, the bound coincides with the achievable region given by Ahlswede et al. (see IEEE Trans. on Inform. Theory, vol.46, no.4, p.1204-16, July 2000), and thus proves the optimality of the coding scheme proposed in it.