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 networksimilarity methods exist; and it is unclear how one should select from amongst them. We provide the first empirical study on the relationships between different networksimilarity 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 can be closely approximated by a much simpler method, and (3) a few network-similarity methods produce rankings that are very close to the consensus ranking.