# Network Geometry

arXiv: https://arxiv.org/abs/2001.03241 · HTML: https://mlsanity.com/paper/2001.03241/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2020.

## Built on by (most cited first, 30 of 31)

- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [MFTraj: Map-Free, Behavior-Driven Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/2405.01266/) (2024)
- [Curvature Graph Generative Adversarial Networks](https://mlsanity.com/paper/2203.01604/) (2022)
- [Learning Harmonic Molecular Representations on Riemannian Manifold](https://mlsanity.com/paper/2303.15520/) (2023)
- [The Autodidactic Universe](https://mlsanity.com/paper/2104.03902/) (2021)
- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [A Recommendation Approach based on Similarity-Popularity Models of Complex Networks](https://mlsanity.com/paper/2210.07816/) (2022)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Scalable Graph Compressed Convolutions](https://mlsanity.com/paper/2407.18480/) (2024)
- [Survey of Generative Methods for Social Media Analysis](https://mlsanity.com/paper/2112.07041/) (2021)
- [Representation Learning on Heterostructures via Heterogeneous Anonymous Walks](https://mlsanity.com/paper/2201.06972/) (2022)
- [An Approach for Link Prediction in Directed Complex Networks based on Asymmetric Similarity-Popularity](https://mlsanity.com/paper/2207.07399/) (2022)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Constructing material network representations for intelligent amorphous alloys design](https://mlsanity.com/paper/2507.16336/) (2025)
- [Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis](https://mlsanity.com/paper/2509.08350/) (2025)
- [Twinning Complex Networked Systems: Data-Driven Calibration of the mABCD Synthetic Graph Generator](https://mlsanity.com/paper/2602.02044/) (2026)
- [A Complex Network based Graph Embedding Method for Link Prediction](https://mlsanity.com/paper/2209.04884/) (2022)
- [A Sequence-Aware Recommendation Method Based on Complex Networks](https://mlsanity.com/paper/2210.07814/) (2022)
- [Hyperbolic Benchmarking Unveils Network Topology-Feature Relationship in GNN Performance](https://mlsanity.com/paper/2406.02772/) (2024)
- [Connecting the geometry and dynamics of many-body complex systems with message passing neural operators](https://mlsanity.com/paper/2502.15913/) (2025)
- [Cellular Development Follows the Path of Minimum Action](https://mlsanity.com/paper/2504.08096/) (2025)
- [PR-CapsNet: Pseudo-Riemannian Capsule Network with Adaptive Curvature Routing for Graph Learning](https://mlsanity.com/paper/2512.08218/) (2025)
- [A Complexity Measure for Active Learning in Multi-group Mean Estimation](https://mlsanity.com/paper/2606.14690/) (2026)
- [Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalization](https://mlsanity.com/paper/2607.27767/) (2026)
- [Hyperbolic Graph Embedders for Link Prediction and Topology Reconstruction](https://mlsanity.com/paper/2608.07029/) (2026)

## Abstract (arXiv)

Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are all intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale-invariance, self-similarity, and other forms of fundamental symmetries in networks. Network geometry is also of great utility in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet. Here, we review the most important theoretical and practical developments dealing with these approaches to network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.