A comment on Doreian's regular equivalence in symmetric structures

It is argued that Patrick Doreian's solution (see SA 36:1/88T1135) to the problem of running REGE ([regular equivalence] see White, Douglas R., "REGGE: A REGular Graph Equivalence Algorithm for Computing Role Distances prior to Blockmodeling," unpublished manuscript, U of California, Irvine, 1984) on symmetric matrices is creative & practical -- if there really is a problem. It is shown that, though Doreian's solution implements a strengthening of REGE that enables it to find meaningful structure in symmetric graphs, it is not a new algorithm for finding maximal REGEs; indeed, it cannot be determined that the method always finds the same equivalence. It is suggested that the detection of REGE should be treated as a hierarchical clustering problem; recommendations for handling symmetric & asymmetric data are offered. In Borgatti Toppings on Doreian Splits: Reflections on Regular Equivalence, Patrick Doreian (U of Pittsburgh, Pa) agrees with the idea of a hierarchy of nested regular equivalence partitions, but expresses new reservations about REGE itself. It is demonstrated that, while the splitting of a symmetric relation into two asymmetric relations does use measures of centrality, it is not clear that the procedure is as responsive as Borgatti suggests. It is concluded that the Doreian split can be viewed as both a response to a specific problem that arises in symmetric (& nonsymmetric) graphs & as an ad hoc adjustment where symmetric input is cut into two asymmetric graphs. 5 Tables, 9 Figures, 18 References. K. Hyatt