Measuring Partial Balance in Signed Networks

TL;DR

This paper evaluates various measures of partial balance in signed networks, comparing their properties and effectiveness on synthetic and real-world datasets to recommend best practices for future research.

Contribution

It formalizes and compares multiple measures of partial balance, analyzing their properties and performance on diverse datasets to guide future applications.

Findings

Some measures outperform others in axiomatic tests

Different measures yield substantially different partial balance levels

Recommendations provided for selecting measures in future studies

Abstract

Is the enemy of an enemy necessarily a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be "balanced" were obtained around 1960. Since then the idea that signed networks tend over time to become more balanced has been widely used in several application areas. However, investigation of this hypothesis has been complicated by the lack of a standard measure of partial balance, since complete balance is almost never achieved in practice. We formalize the concept of a measure of partial balance, discuss various measures, compare the measures on synthetic datasets, and investigate their axiomatic properties. The synthetic data involves Erd\H{o}s-R\'enyi and specially structured random graphs. We show that some measures behave better than others in terms of axioms and ability to differentiate between graphs. We also use well-known datasets from the sociology and biology literature, such as Read's New Guinean tribes, gene regulatory networks related to two organisms, and a network involving senate bill co-sponsorship. Our results show that substantially different levels of partial balance is observed under cycle-based, eigenvalue-based, and frustration-based measures. We make some recommendations for measures to be used in future work.