Positive contagion and the macrostructures of generalized balance

Noah E Friedkin,Anton V Proskurnikov,Francesco Bullo

doi:10.1017/nws.2019.19

Noah E Friedkin, Anton V Proskurnikov + Show 1 more

Open Access

https://doi.org/10.1017/nws.2019.19

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Abstract

AbstractBalance theory has advanced with interdisciplinary contributions from social science, physical science, engineering, and mathematics. The common focus of attention is social networks in which every individual has either a positive or negative, cognitive or emotional, appraisal of every other individual. The current frontier of work on balance theory is a hunt for a dynamical model that predicts the temporal evolution of any such appraisal network to a particular structure in the complete set of balanced networks allowed by the theory. Finding such a model has proved to be a difficult problem. In this article, we contribute a parsimonious solution of the problem that explicates the conditions under which a network will evolve either to a set of mutually antagonistic cliques or to an asymmetric structure that allows agreement, cooperation, and compromise among cliques.

Highlights

The broad interest in balance theory is based on one of its special cases: a group in which every individual has a list of friends and enemies and belongs to one of two mutually antagonistic cliques, parties, or factions
This assumption eliminates all but 4 of the 16 possible types of triads, and the problem complexity is reduced to a mechanism that eliminates triads with three symmetric negative relations or two symmetric positive relations
Symmetric relations are an emergent condition restricted to cliques, which might be connected by asymmetric relations

Summary

Introduction

The broad interest in balance theory is based on one of its special cases: a group in which every individual has a list of friends and enemies and belongs to one of two mutually antagonistic cliques, parties, or factions. The empirical evidence shows that appraisal network evolution is not reliably governed by rules 1–3 and instead is mainly based on the elimination of violations of transitivity These findings triggered the development of generalized balance theory, which allows all nine types of triads that do not violate transitivity in contrast to classic balance, which is constrained to two types of triads. An attractive implication of this mechanism is that graph theory’s four topological categories of networks (strong, unilateral, weak, and disconnected) are categorical distinctions that transfer to the class of balanced condensed macrostructures generated by it, and that each such class is associated with a distinctive set of allowed triads In this framework, the focal Harary and Cartwright (1956) case of classic balance evolves from a disconnected G with two strong components.

Graph-theoretic preliminaries

Positive contagion

Classes of balanced condensed macrostructures

Discussion