Cumulated social roles: The duality of persons and their algebras

Ronald L. Breiger, Philippa E. Pattison

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


The study of social roles from the perspectives of individual actors, and the relation of graph homomorphisms to semigroup homomorphisms, have been the two most prominent topics to emerge from the recent resurgence of progress made on the algebraic analysis of social networks. Through our central construction, the cumulated person hierarchy, we present a framework for elaborating and extending these two lines of research. We focus on each actor in turn as ego, and we articulate what we believe to be the fundamental duality of persons and their algebras. We derive graph and semigroup homomorphisms for three algebras containing 81, 43, and 93 elements, respectively. Throughout, our discussion of theoretical issues is oriented toward an empirical application to the Padgett data set on conspiracy and faction in Renaissance Florence.

Original languageEnglish (US)
Pages (from-to)215-256
Number of pages42
JournalSocial Networks
Issue number3
StatePublished - Sep 1986

ASJC Scopus subject areas

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


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