Iterated roles: Mathematics and application

Stephen P. Borgatti, John Boyd, Martin Evertt

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Recent work by Borgatti and Everett (1989) has shown that the collection of regular equivalences described by White and Reitz (1983) forms a lattice. In this paper, we present a procedure called iterated roles for tracing systematic paths through the lattice. At the heart of iterated roles is the proof that the regular equivalence of a regular equivalence is itself regular. The procedure enables us to find several otherwise unknown regular equivalences, including an extension of automorphic equivalence (Everett 1985) that is not sensitive to degree. A key benefit of iterated roles is the generation of sequences of hierarchically nested equivalences. This capability suggests an approach to role structure analysis in which one examines not just one blocking of actors but a series of increasingly broad simplifications of the data. Consequently, we are able to (a) choose the level of simplification that proves most illuminating, and (b) view both to broad structural outlines of the data and the finer details simultaneously.

Original languageEnglish
Pages (from-to)159-172
Number of pages14
JournalSocial Networks
Issue number2
StatePublished - Jun 1989

ASJC Scopus subject areas

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


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