# Balance in signed networks

arXiv: https://arxiv.org/abs/1809.05140 · HTML: https://mlsanity.com/paper/1809.05140/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [Signed Bipartite Graph Neural Networks](https://mlsanity.com/paper/2108.09638/) (2021)
- [Signed Diverse Multiplex Networks: Clustering and Inference](https://mlsanity.com/paper/2402.10242/) (2024)
- [Adversarial Robustness of Link Sign Prediction in Signed Graphs](https://mlsanity.com/paper/2401.10590/) (2024)
- [Signed graphs in data sciences via communicability geometry](https://mlsanity.com/paper/2403.07493/) (2024)
- [Signed Graph Learning: Algorithms and Theory](https://mlsanity.com/paper/2507.09717/) (2025)

## Abstract (arXiv)

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.