The class of all regular equivalences: Algebraic structure and computation

Stephen P. Borgatti, Martin G. Everett

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


In this paper, we explore the structure of the set of all regular equivalences (White and Reitz 1983), proving that it forms a lattice, and suggest a general approach to computing certain elements of the lattice. The resulting algorithm represents a useful complement to the White and Reitz algorithm, which can only find the maximal regular equivalence of a graph. Using this algorithm, it is possible to compute several well-known equivalences, such as structural equivalence (Lorrain and White 1971), automorphic equivalence (Everett and Borgatti 1988), and Winship-Pattison equivalence (Winship and Mandel 1983). In addition, any number of other useful equivalences may be generated, providing suitable mathematical descriptions of them are available.

Original languageEnglish
Pages (from-to)65-88
Number of pages24
JournalSocial Networks
Issue number1
StatePublished - Mar 1989

ASJC Scopus subject areas

  • Anthropology
  • Sociology and Political Science
  • General Social Sciences
  • General Psychology


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