Abstract
Abstract This paper extends Compositional Equivalence – which is a structural correspondence type intended for multiplex networks – by incorporating actor attributes in the modeling of the network relational structure as diagonal matrices. As an illustration, we construct the positional system of the Florentine families network with Business and Marriage ties together with relevant characteristics acquired from the actors such as the families’ financial Wealth and the number of Priorates they held. Different representations of the cumulated person hierarchies reveal that adding Wealth to the modeling provides a more accurate picture of what the substantial narrative says about this network.
Highlights
Relationships among actors in a defined collective scheme are the primary source of information for social network analysis
These sorts of arrangements are known as multiplex networks, and the associated relational structure of such social systems is typically reduced onto positional systems to facilitate a useful substantial interpretation
Connections network structure without dropping the relational differentiation, and we extend the positional analysis to non-ascribed characteristics of the actors in the network, which are included as generator relations in the form of diagonal matrices
Summary
Relationships among actors in a defined collective scheme are the primary source of information for social network analysis. A key issue in the reduction process is to preserve the multiplicity of the ties since the way different ties are intertwined provides important information about the network structure In this spirit, Breiger and Pattison (1986) proposed a type of equivalence among the network members that is built on local role algebras for the creation of the positional system. Examples of actor attributes are the acquisition of a certain characteristic from the social environment such as innovation adoption; the acquisition of a certain attitude; the non-compulsory affiliation to a group; the individual’s personal wealth and political power, etc Such attributes can play a significant role in the network relational structure and should be incorporated into the modeling process
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