A Guide to Selecting a Network Similarity Method

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 di↵erent 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) di↵erent 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.