Methodology and Statistics
International Conference, 24 - 27 September 2000
Hotel Bor and Castle Hrib, Preddvor, Slovenia

Computing Regular Equivalence:
practical and theoretical issues.

Martin Everett
School of Computing and Mathematical Sciences
The University of Greenwich

Social network analysts have tried to capture the idea of social role explicitly by proposing a framework that precisely gives conditions under which grouped actors are playing equivalent roles. They term these methods postional 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 no efficient algorithms to test whether there is a regular k-partition. That is a partition into 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 been 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.

Key words: regular partitions