# Signed graphs in data sciences via communicability geometry

arXiv: https://arxiv.org/abs/2403.07493 · HTML: https://mlsanity.com/paper/2403.07493/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 107 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 22 of 22)

- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Quantifying Controversy in Social Media](https://mlsanity.com/paper/1507.05224/) (2015)
- [A Survey of Signed Network Mining in Social Media](https://mlsanity.com/paper/1511.07569/) (2015)
- [SPONGE: A generalized eigenproblem for clustering signed networks](https://mlsanity.com/paper/1904.08575/) (2019)
- [Discovering Polarized Communities in Signed Networks](https://mlsanity.com/paper/1910.02438/) (2019)
- [Nonparametric weighted stochastic block models](https://mlsanity.com/paper/1708.01432/) (2017)
- [Learning Stance Embeddings from Signed Social Graphs](https://mlsanity.com/paper/2201.11675/) (2022)
- [On spectral partitioning of signed graphs](https://mlsanity.com/paper/1701.01394/) (2017)
- [Spreading and Structural Balance on Signed Networks](https://mlsanity.com/paper/2212.10158/) (2022)
- [Balance in signed networks](https://mlsanity.com/paper/1809.05140/) (2018)
- [Stochastic block model and exploratory analysis in signed networks](https://mlsanity.com/paper/1501.00594/) (2015)
- [Balance and Frustration in Signed Networks](https://mlsanity.com/paper/1712.04628/) (2017)
- [Identifying hidden coalitions in the US House of Representatives by optimally partitioning signed networks based on generalized balance](https://mlsanity.com/paper/2105.01913/) (2021)
- [Geometry of Similarity Comparisons](https://mlsanity.com/paper/2006.09858/) (2020)
- [Introduction to correlation networks: Interdisciplinary approaches beyond thresholding](https://mlsanity.com/paper/2311.09536/) (2023)
- [Applications of Structural Balance in Signed Social Networks](https://mlsanity.com/paper/1402.6865/) (2014)
- [Multiple Partitioning of Multiplex Signed Networks: Application to European Parliament Votes](https://mlsanity.com/paper/1811.10337/) (2018)
- [Polarization and multiscale structural balance in signed networks](https://mlsanity.com/paper/2303.16774/) (2023)
- [Signed Graph Analysis for the Interpretation of Voting Behavior](https://mlsanity.com/paper/1712.10157/) (2017)
- [Partitioning signed networks](https://mlsanity.com/paper/1803.02082/) (2018)
- [Loss of structural balance in stock markets](https://mlsanity.com/paper/2104.06254/) (2021)
- [Network bypasses sustain complexity](https://mlsanity.com/paper/2207.06813/) (2022)

## Abstract (arXiv)

Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for signed graphs and explore in depth its mathematical properties. We also prove that the communicability induces a hyperspherical geometric embedding of the signed network, and derive communicability-based metrics that satisfy the axioms of a distance even in the presence of negative edges. We then apply these metrics to solve several problems in the data analysis of signed graphs within a unified framework. These include the partitioning of signed graphs, dimensionality reduction, finding hierarchies of alliances in signed networks, and quantifying the degree of polarization between the existing factions in social systems represented by these types of graphs.