Review

Check out our latest pre-print, Signed Networks: theory, methods, and applications !

https://doi.org/10.48550/arXiv.2511.17247

Outline

1. Introduction
2. Mathematical foundations of signed networks
   1. Definition and representation of signed networks
   2. Basic metrics
      1. Signed degree and its distribution
      2. Signed clustering coefficient
      3. Signed distances
      4. Signed centralities
      5. Signed motifs
   3. Signed Laplacian
3. Cognitive and structural balance
   1. Heiderian (cognitive) balance
   2. Hararian (structural) balance
   3. Comparison between Heiderian and Hararian balance
   4. Mathematical properties of balanced networks
   5. Balance indices
4. Network structure and inference
   1. Null models
   2. Node embeddings
   3. Sign prediction
   4. Community detection
      1. Quality function optimization
      2. Spectral methods
      3. Statistical inference
5. Dynamics
   1. Dynamics on networks
      1. Diffusive dynamics
      2. Voter model and random walks
      3. Compartmental models
      4. Cascade and threshold models
      5. Other dynamics
   2. Dynamics of networks: evolving networks
      1. Toy models of signed networks dynamics
      2. Data-driven approaches
      3. Mechanisms governing signed network dynamics
   3. Co-evolving dynamics
6. Collection, inference and availability of signed data
   1. Mining signed networks from raw data
      1. Ranking data
      2. Unsigned bipartite networks
      3. Aggregates of unsigned interaction data
      4. Sparse online interactions
   2. Common data sources
      1. In-person social communities
      2. Online platforms
      3. Political systems
      4. Country systems
7. Myths and pitfalls
8. Conclusions
9. Appendix

Cite it as:

@misc{signednetworksreview,
      title={Signed Networks: theory, methods, and applications}, 
      author={Fernando Diaz-Diaz and Elena Candellone and Miguel A. Gonzalez-Casado and Emma Fraxanet and Antoine Vendeville and Irene Ferri and Andreia Sofia Teixeira},
      year={2025},
      eprint={2511.17247},
      archivePrefix={arXiv},
      primaryClass={physics.soc-ph},
      url={https://arxiv.org/abs/2511.17247}, 
}