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We consider the problem of determining how similar two networks (without known node-correspondences) are. This problem occurs frequently in real-world applications such as transfer learning and change detection. Many network-similarity methods exist; and it is unclear how one should select from amongst them. We provide the first empirical study on the relationships between different network-similarity methods. Specifically, we present (1) an approach for identifying groups of comparable network-similarity methods and (2) an approach for computing the consensus among a given set of network-similarity methods. We compare and contrast twenty network-similarity methods by applying our approaches to a variety of real datasets spanning multiple domains. Our experiments demonstrate that (1) different network-similarity methods are surprisingly well correlated, (2) some complex network-similarity methods …