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The role assignment model nearly fits most social networks

Publication ,  Journal Article
Pekeč, A; Roberts, FS
Published in: Mathematical social sciences
May 1, 2001

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. © Elsevier Science B.V.

Duke Scholars

Published In

Mathematical social sciences

DOI

ISSN

0165-4896

Publication Date

May 1, 2001

Volume

41

Issue

3

Start / End Page

275 / 293

Related Subject Headings

  • Economic Theory
  • 49 Mathematical sciences
  • 44 Human society
  • 38 Economics
  • 16 Studies in Human Society
  • 14 Economics
  • 01 Mathematical Sciences
 

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Pekeč, A., & Roberts, F. S. (2001). The role assignment model nearly fits most social networks. Mathematical Social Sciences, 41(3), 275–293. https://doi.org/10.1016/S0165-4896(00)00064-0
Pekeč, A., and F. S. Roberts. “The role assignment model nearly fits most social networks.” Mathematical Social Sciences 41, no. 3 (May 1, 2001): 275–93. https://doi.org/10.1016/S0165-4896(00)00064-0.
Pekeč A, Roberts FS. The role assignment model nearly fits most social networks. Mathematical social sciences. 2001 May 1;41(3):275–93.
Pekeč, A., and F. S. Roberts. “The role assignment model nearly fits most social networks.” Mathematical Social Sciences, vol. 41, no. 3, May 2001, pp. 275–93. Scopus, doi:10.1016/S0165-4896(00)00064-0.
Pekeč A, Roberts FS. The role assignment model nearly fits most social networks. Mathematical social sciences. 2001 May 1;41(3):275–293.
Journal cover image

Published In

Mathematical social sciences

DOI

ISSN

0165-4896

Publication Date

May 1, 2001

Volume

41

Issue

3

Start / End Page

275 / 293

Related Subject Headings

  • Economic Theory
  • 49 Mathematical sciences
  • 44 Human society
  • 38 Economics
  • 16 Studies in Human Society
  • 14 Economics
  • 01 Mathematical Sciences