# Network Geometry Inference using Common Neighbors

arXiv: https://arxiv.org/abs/1502.05578 · HTML: https://mlsanity.com/paper/1502.05578/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2015.

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

- [Highly Scalable and Provably Accurate Classification in Poincare Balls](https://mlsanity.com/paper/2109.03781/) (2021)
- [Not All Neighbors Are Worth Attending to: Graph Selective Attention Networks for Semi-supervised Learning](https://mlsanity.com/paper/2210.07715/) (2022)
- [HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering](https://mlsanity.com/paper/2205.09721/) (2022)
- [Provably Accurate and Scalable Linear Classifiers in Hyperbolic Spaces](https://mlsanity.com/paper/2203.03730/) (2022)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Lower Ricci Curvature for Hypergraphs](https://mlsanity.com/paper/2506.03943/) (2025)
- [Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detection](https://mlsanity.com/paper/2512.18826/) (2025)
- [Hyperbolic Graph Embedders for Link Prediction and Topology Reconstruction](https://mlsanity.com/paper/2608.07029/) (2026)

## Abstract (arXiv)

We introduce and explore a new method for inferring hidden geometric coordinates of nodes in complex networks based on the number of common neighbors between the nodes. We compare this approach to the HyperMap method, which is based only on the connections (and disconnections) between the nodes, i.e., on the links that the nodes have (or do not have). We find that for high degree nodes the common-neighbors approach yields a more accurate inference than the link-based method, unless heuristic periodic adjustments (or "correction steps") are used in the latter. The common-neighbors approach is computationally intensive, requiring O(t4) running time to map a network of t nodes, versus O(t3) in the link-based method. But we also develop a hybrid method with O(t3) running time, which combines the common-neighbors and link-based approaches, and explore a heuristic that reduces its running time further to O(t2), without significant reduction in the mapping accuracy. We apply this method to the Autonomous Systems (AS) Internet, and reveal how soft communities of ASes evolve over time in the similarity space. We further demonstrate the method's predictive power by forecasting future links between ASes. Taken altogether, our results advance our understanding of how to efficiently and accurately map real networks to their latent geometric spaces, which is an important necessary step towards understanding the laws that govern the dynamics of nodes in these spaces, and the fine-grained dynamics of network connections.