Document Type

Post-Print

Publication Date

12-2017

Subjects

Cooperation Mathematical models

Abstract

Since the 1940s there has been an interest in the question of why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an introduction to the notion of social balance and a new (and simplified) analysis of that model. This new analysis allows us to choose general initial conditions, as opposed to the symmetric ones previously considered. We show that for general initial conditions, four factions will evolve instead of two. We characterize the four factions, and give an idea of their relative sizes.

Description

© THE MATHEMATICAL ASSOCIATION OF AMERICA

This is the author’s version of a work that was accepted for publication in American Mathematical Monthly. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

Persistent Identifier

https://archives.pdx.edu/ds/psu/25482

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