Document Type
Post-Print
Publication Date
12-2017
Subjects
Cooperation -- Mathematical models, Social networks -- Mathematical models -- Analysis, Directed graphs
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.
Persistent Identifier
https://archives.pdx.edu/ds/psu/25482
Citation Details
Veerman, J. J. P., "Social Balance and the Bernoulli Equation" (2017). Mathematics and Statistics Faculty Publications and Presentations. 209.
https://archives.pdx.edu/ds/psu/25482
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.