# Topological implications of negative curvature for biological and social networks

arXiv: https://arxiv.org/abs/1403.1228 · HTML: https://mlsanity.com/paper/1403.1228/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2014.

## Built on by (most cited first, 4 of 4)

- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [Hyperbolic Genome Embeddings](https://mlsanity.com/paper/2507.21648/) (2025)
- [Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension](https://mlsanity.com/paper/2509.13385/) (2025)

## Abstract (arXiv)

Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity) to parameterized finite networks, and show that a variety of biological and social networks are hyperbolic. This hyperbolicity property has strong implications on the higher-order connectivity and other topological properties of these networks. Specifically, we derive and prove bounds on the distance among shortest or approximately shortest paths in hyperbolic networks. We describe two implications of these bounds to cross-talk in biological networks, and to the existence of central, influential neighborhoods in both biological and social networks.