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One of the major challenges in evolutionary ecology is to understand how coevolution shapes species interaction networks. Important topological properties of networks such as nestedness and modularity are thought to be affected by coevolution. However, there has been no test whether coevolution does, in fact, lead to predictable network structure. Here, we investigate the structure of simulated bipartite networks generated under different modes of coevolution. We ask whether evolutionary processes influence network structure and, furthermore, whether any emergent trends are influenced by the strength or "intimacy" of the species interactions. We find that coevolution leaves a weak and variable signal on network topology, particularly nestedness and modularity, which was not strongly affected by the intimacy of interactions. Our findings indicate that network metrics, on their own, should not be used to make inferences about processes underlying the evolutionary history of communities. Instead, a more holistic approach that combines network approaches with traditional phylogenetic and biogeographic reconstructions is needed.