Compositional Equivalence with actor attributes: Positional analysis of the the Florentine Families network

TL;DR

This paper enhances the Compositional Equivalence method for multiplex networks by integrating actor attributes like wealth and priors, demonstrated through a historical Florentine families network analysis.

Contribution

It introduces a novel way to incorporate actor attributes into the structural analysis of multiplex networks using diagonal matrices.

Findings

Including Wealth improves the accuracy of the network's positional analysis.

Actor attributes significantly influence the network's structural interpretation.

The method provides a richer understanding of the Florentine families' social and economic ties.

Abstract

This paper extends Compositional Equivalence ---which is a structural correspondence type aimed for multiplex networks--- by incorporating actor attributes in the modelling of the network relational structure as diagonal matrices. As an illustration, we construct the positional system of the Florentine families' network in the 15th century with Business and Marriage ties together with relevant characteristics acquired from the actors such as families' financial Wealth and their number of Priorates. Different representations of the cumulated person hierarchies reveal that adding Wealth in the modelling provides a more accurate picture of what the substantial narrative says about this network.