The role assignment model nearly fits most social networks

Aleksandar Pekeč, Fred S. Roberts

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Role assignments, introduced by Everett and Borgatti [Mathematical Social Sciences 26 (1991) 183], who called them role colorings, formalize the idea, arising in the theory of social networks, that individuals of the same social role will relate in the same way to individuals playing counterpart roles. If G is a graph, a k-role assignment is a surjective function mapping each vertex into a positive integer 1,2,...,k, so that if x and y have the same role, then the sets of roles assigned to their neighbors are the same. We show that all graphs G having no astronomical discrepancies between the minimum and the maximum degree have a k-role assignment. Furthermore, we introduce and study a natural measure expressing how close an onto map f:V(G)→{1,...,k} is to being a k-role assignment of a graph G=(V,E), and show that almost all graphs nearly have a k-role assignment.

Original languageEnglish (US)
Pages (from-to)275-293
Number of pages19
JournalMathematical social sciences
Issue number3
StatePublished - May 2001

All Science Journal Classification (ASJC) codes

  • Sociology and Political Science
  • General Social Sciences
  • General Psychology
  • Statistics, Probability and Uncertainty


  • C60
  • C78
  • Role assignment
  • Role coloring
  • Social networks
  • Social role


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