Positional Analysis of Multiple Networks with Actor Attributes

This paper extends the notion of Compositional Equivalence for multiple networks developed by Breiger and Pattison (1986) by providing with an effective way to include actor attributes in their relational structures. The relevant characteristics acquired from the actors are integrated into a single partially ordered semigroup structure that relates both ties and actor attributes in the network at an aggregated level. In line with the approach by the mentioned authors, we illustrate the modelling process with the Florentine families’ network dataset with an extended substantial interpretation of this banking set-up through the role interlock of the system and the diverse algebraic constraints governing the role structure.