TY - JOUR
T1 - The class of all regular equivalences
T2 - Algebraic structure and computation
AU - Borgatti, Stephen P.
AU - Everett, Martin G.
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1989/3
Y1 - 1989/3
N2 - 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.
AB - 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.
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U2 - 10.1016/0378-8733(89)90018-X
DO - 10.1016/0378-8733(89)90018-X
M3 - Article
AN - SCOPUS:34247763755
SN - 0378-8733
VL - 11
SP - 65
EP - 88
JO - Social Networks
JF - Social Networks
IS - 1
ER -