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Regular Equivalence

 

Regular equivalence is an attempt to capture the sociological notion of a relational or structural role. Two nodes are said to play the same role (i.e., are regularly equivalent) if the have ties to the same roles. For example, two nurses will have similar types of relations (as each other) to doctors, patients, other nurses, and so on. Similarly, two patients tend to have similar relations as each other with doctors, nurses, etc. Important note: the equivalent actors has the same types of relations with equivalent others, but not necessarily the same others.

 

Topics

  • Lattice of regular equivalences

  • Profile similarity methods (REGE)

  • Blockmodeling methods

Readings

  • White, D. and Reitz, K. 1983 Graph and Semigroup Homomorphisms. Social Networks 5:193-234 [pdf]

  • Borgatti, S. P., & Everett, M. G. 1992. Notions of position in social network analysis. Sociological Methodology, 22: 1-35. [pdf]

  • Borgatti, S. P., & Everett, M. G. 1992. Graph colorings and power in experimental exchange networks. Social Networks, 14: 287-308. [pdf]

  • Krackhardt, D. & Porter, L. 1986. The snowball effect: Turnover embedded in communication networks. Journal of Applied Psychology 71: 50-55. [pdf]

  

Tutorials

Exercises

Handouts

Slides

 

Concepts

  • White, D. and Reitz, K. 1983 Graph and Semigroup Homomorphisms. Social Networks 5:193-234 [pdf]
  • Everett, M.G., & Borgatti, S. P. 1994. Regular equivalence: General theory. Journal of Mathematical Sociology, 19(1): 29-52. [pdf]]
  • White, D. R. and K. P. Reitz. 1989. "Re-Thinking the Role Concept: Homomorphisms on Social Networks." Pp. 429-88 in Research Methods in Social Network Analysis, Editors L. C. Freeman, D. R. White, and A. K. Romney. Fairfax, VA: George Mason University Press
  • Nadel, SF A Theory of Social Structure, particularly Chapter 4.
  • J. Reichardt,a and D.R. White. 2007. Role models for complex networks. European Physical Journal B 60: 217-224 [^pdf]

Applications

  • Krackhardt, D. & Porter, L. 1986. The snowball effect: Turnover embedded in communication networks. Journal of Applied Psychology 71: 50-55. [pdf]
  • Luczkovich, J.J., Borgatti, S.P., Johnson, J.C. and Everett , M.G. 2003. Defining and Measuring Trophic Role Similarity in Food Webs Using Regular Equivalence. Journal of Theoretical Biology. 220(3): 303-321. [pdf]
  • J. Reichardt,a and D.R. White. 2007. Role models for complex networks. highlighTS froMEUroPEAN joUrNAlS. [^pdf]
  • Smith, D. A. and D. R. White. 1992. "Structure and Dynamics of the Global Economy: Network Analysis of International Trade 1965-1980." Social Forces 70:857-93. 

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