# Dynamics over Signed Networks

arXiv: https://arxiv.org/abs/1706.03362 · HTML: https://mlsanity.com/paper/1706.03362/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2017.

## Built on by (most cited first, 8 of 8)

- [LLM-based multi-agent poetry generation in non-cooperative environments](https://mlsanity.com/paper/2409.03659/) (2024)
- [Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics](https://mlsanity.com/paper/2312.11198/) (2023)
- [Large Language Models can Achieve Social Balance](https://mlsanity.com/paper/2410.04054/) (2024)
- [A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNs](https://mlsanity.com/paper/2502.11394/) (2025)
- [Weaver: Kronecker Product Approximations of Spatiotemporal Attention for Traffic Network Forecasting](https://mlsanity.com/paper/2511.08888/) (2025)
- [Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization](https://mlsanity.com/paper/2604.05042/) (2026)
- [Joint Learning of Network Topology and Opinion Dynamics Based on Bandit Algorithms](https://mlsanity.com/paper/2306.15695/) (2023)
- [Exploring Oversmoothing with Householder Matrices](https://mlsanity.com/paper/2608.12514/) (2026)

## Abstract (arXiv)

A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two different types of interactions take place along the positive and negative links, respectively, arise from various biological, social, political, and economic systems. As modifications to the conventional DeGroot dynamics for positive links, two basic types of negative interactions along negative links, namely the opposing rule and the repelling rule, have been proposed and studied in the literature. This paper reviews a few fundamental convergence results for such dynamics over deterministic or random signed networks under a unified algebraic-graphical method. We show that a systematic tool of studying node state evolution over signed networks can be obtained utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions.