Balance in signed networks

TL;DR

This paper introduces two measures of structural balance in signed networks, demonstrating their effectiveness in assessing real-world networks and predicting unknown edge signs better than chance.

Contribution

It proposes new measures of balance based on weak and strong balance concepts and evaluates their performance on real-world signed networks.

Findings

Real-world signed networks are significantly balanced according to the measures.

The measures outperform chance in predicting unknown edge signs.

Balance measures are consistent across different tasks and datasets.

Abstract

We consider signed networks in which connections or edges can be either positive (friendship, trust, alliance) or negative (dislike, distrust, conflict). Early literature in graph theory theorized that such networks should display "structural balance," meaning that certain configurations of positive and negative edges are favored and others are disfavored. Here we propose two measures of balance in signed networks based on the established notions of weak and strong balance, and compare their performance on a range of tasks with each other and with previously proposed measures. In particular, we ask whether real-world signed networks are significantly balanced by these measures compared to an appropriate null model, finding that indeed they are, by all the measures studied. We also test our ability to predict unknown signs in otherwise known networks by maximizing balance. In a series of cross-validation tests we find that our measures are able to predict signs substantially better than chance.