Ego‐centered and local roles: A graph theoretic approach

Structural equivalence (Lorrain and White, 1971) and automorphic equivalence (Everett, 1985) are generalized to define neighborhood‐ and ego‐centered equivalences. It is shown that local versions of these equivalences can then be formulated quite naturally. In addition to these natural localizations, a generalized procedure capable of localizing any model of role equivalence is presented. From a theoretical point of view, local roles are recommended by the notion that network influences on ego diminish with distance. From a practical point of view, local roles help find structure in graphs where global equivalences find no two actors equivalent.