# Computing regular equivalence: practical and theoretical issues

Everett, Martin and Borgatti, Stephen
(2002)
*Computing regular equivalence: practical and theoretical issues.*
In: Mrvar, Andrej and Ferligoj, Anuška, (eds.)
Developments in Statistics.
Metodoloski Zvezki
(17).
Faculty of Social Sciences, University of Ljubljana, Slovenia, Ljubljana, Slovenia, pp. 31-42.
ISBN 9612350906

## Abstract

Social network analysts have tried to capture the idea of social role explicitly by proposing a framework that precisely gives conditions under which group actors are playing equivalent roles. They term these methods positional analysis techniques. The most general definition is regular equivalence which captures the idea that equivalent actors are related in a similar way to equivalent alters. Regular equivalence gives rise to a whole class of partitions on a network. Given a network we have two different computational problems. The first is how to find a particular regular equivalence. An algorithm exists to find the largest regular partition but there are not efficient algorithms to test whether there is a regular k-partition. That is a partition in k groups that is regular. In addition, when dealing with real data, it is unlikely that any regular partitions exist. To overcome this problem relaxations of regular equivalence have been proposed along with optimisation techniques to find nearly regular partitions. In this paper we review the algorithms that have developed to find particular regular equivalences and look at some of the recent theoretical results which give an insight into the complexity of finding regular partitions.

Item Type: | Book Section |
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Additional Information: | [1] Chapter 10 |

Uncontrolled Keywords: | computing, regular equivalence, theory |

Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Computer software |

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

Related URLs: | |

Last Modified: | 14 Oct 2016 09:00 |

URI: | http://gala.gre.ac.uk/id/eprint/565 |

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