What is Similarity (network science)?

Similarity in network analysis occurs when two nodes fall in the same equivalence class.

There are three fundamental approaches to constructing measures of network similarity: structural equivalence, automorphic equivalence, and regular equivalence. There is a hierarchy of the three equivalence concepts: any set of structural equivalences are also automorphic and regular equivalences. Any set of automorphic equivalences are also regular equivalences. Not all regular equivalences are necessarily automorphic or structural; and not all automorphic equivalences are necessarily structural.