# Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs

arXiv: https://arxiv.org/abs/2506.15464 · HTML: https://mlsanity.com/paper/2506.15464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Hyperbolic Category Discovery](https://mlsanity.com/paper/2504.06120/) (2025)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [Temporal Multiresolution Graph Neural Networks For Epidemic Prediction](https://mlsanity.com/paper/2205.14831/) (2022)
- [Poincar'e Differential Privacy for Hierarchy-Aware Graph Embedding](https://mlsanity.com/paper/2312.12183/) (2023)
- [Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approach](https://mlsanity.com/paper/2310.18918/) (2023)
- [DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks](https://mlsanity.com/paper/2310.02027/) (2023)
- [Continuous Geometry-Aware Graph Diffusion via Hyperbolic Neural PDE](https://mlsanity.com/paper/2406.01282/) (2024)
- [Residual Hyperbolic Graph Convolution Networks](https://mlsanity.com/paper/2412.03825/) (2024)
- [Blind Deconvolution of Graph Signals: Robustness to Graph Perturbations](https://mlsanity.com/paper/2412.15133/) (2024)

## Abstract (arXiv)

Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its endpoints drift toward the graph's Gromov boundary. Using Busemann functions on delta-hyperbolic networks, we prove a closed-form upper bound on the operator's spectral norm: every signal loses a curvature-controlled fraction of its energy at each pass. The result delivers a parameter-free, lightweight filter whose stability follows directly from geometric first principles, offering a new analytic tool for graph signal processing on data with dense or hidden hierarchical structure.