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Article
The class of all regular equivalences: Algebraic structure and computation
Social Networks (1989)
  • Stephen P. Borgatti, University of California - Irvine
  • Martin G. Everett
Abstract
In this paper, we explore the structure of the set of all regular equivalences (White and Reitz 1983), proving that it forms a lattice, and suggest a general approach to computing certain elements of the lattice. The resulting algorithm represents a useful complement to the White and Reitz algorithm, which can only find the maximal regular equivalence of a graph. Using this algorithm, it is possible to compute several well-known equivalences, such as structural equivalence (Lorrain and White 1971), automorphic equivalence (Everett and Borgatti 1988), and Winship-Pattison equivalence (Winship and Mandel 1983). In addition, any number of other useful equivalences may be generated, providing suitable mathematical descriptions of them are available.
Publication Date
March, 1989
Citation Information
Stephen P. Borgatti and Martin G. Everett. "The class of all regular equivalences: Algebraic structure and computation" Social Networks Vol. 11 Iss. 1 (1989)
Available at: http://works.bepress.com/steveborgatti/31/