# Spreading and Structural Balance on Signed Networks

arXiv: https://arxiv.org/abs/2212.10158 · HTML: https://mlsanity.com/paper/2212.10158/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2022.

## Built on by (most cited first, 6 of 6)

- [Structural Balance and Random Walks on Complex Networks with Complex Weights](https://mlsanity.com/paper/2307.01813/) (2023)
- [In-Group Love, Out-Group Hate: A Framework to Measure Affective Polarization via Contentious Online Discussions](https://mlsanity.com/paper/2412.14414/) (2024)
- [Signed graphs in data sciences via communicability geometry](https://mlsanity.com/paper/2403.07493/) (2024)
- [Matrix-weighted networks for modeling multidimensional dynamics](https://mlsanity.com/paper/2410.05188/) (2024)
- [Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming](https://mlsanity.com/paper/2506.01826/) (2025)
- [Complex-Weighted Convolutional Networks: Provable Expressiveness via Complex Diffusion](https://mlsanity.com/paper/2511.13937/) (2025)

## Abstract (arXiv)

Two competing types of interactions often play an important part in shaping system behavior, such as activatory or inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. However, the primary focus of the literature is on the unweighted and structurally unbalanced ones, where all cycles have an even number of negative edges. Hence here, we first introduce a classification of signed networks into balanced, antibalanced or strictly unbalanced ones, and then characterize each type of signed networks in terms of the spectral properties of the signed weighted adjacency matrix. In particular, we show that the spectral radius of the matrix with signs is smaller than that without if and only if the signed network is strictly unbalanced. These properties are important to understand the dynamics on signed networks, both linear and nonlinear ones. Specifically, we find consistent patterns in a linear and a nonlinear dynamics theoretically, depending on their type of balance. We also propose two measures to further characterize strictly unbalanced networks, motivated by perturbation theory. Finally, we numerically verify these properties through experiments on both synthetic and real networks.