# Relations, residuals, regular interiors, and relative regular equivalence

Boyd, John P. and Everett, Martin G.
(1999)
*Relations, residuals, regular interiors, and relative regular equivalence.*
Social Networks, 21 (2).
pp. 147-165.
ISSN 0378-8733
(doi:10.1016/S0378-8733(99)00006-4)

## Abstract

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Item Type: | Article |
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Uncontrolled Keywords: | relations, residuals, regular interiors, relative regular equivalence |

Subjects: | Q Science > QA Mathematics |

Pre-2014 Departments: | School of Business School of Computing & Mathematical Sciences |

Related URLs: | |

Last Modified: | 14 Oct 2016 09:00 |

URI: | http://gala.gre.ac.uk/id/eprint/379 |

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