Structural similarity, semigroups and idempotents

Derived from the notion of structural equivalence proposed by Francois Lorrain & Harrison C. White (see SA 20:3/72F4686), it is proposed that structural equivalence can be termed an "idempotent," or an element "r" of a semigroup S composed of the observed relations among individuals; this algebraic approach simplifies the procedures used in network analysis. Idempotents are transitive (although the reverse is not necessarily true). Also presented is an algorithm for figuring out an idempotent associated with any given relation. The procedure is supported by eight theorems demonstrating graphs, the notion of structural similarity, & other situations. 13 References. D. Dunseath.