Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs
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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.
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References · 12
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
- 2022Graph neural networks for materials science and chemistrycited by 182
- 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 50
- 2025Hyperbolic Category Discoverycited by 20
- 2023HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Predictioncited by 14
- 2022Temporal Multiresolution Graph Neural Networks For Epidemic Predictioncited by 11
- 2023Poincar'e Differential Privacy for Hierarchy-Aware Graph Embeddingcited by 7
- 2023Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approachcited by 5
- 2023DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networkscited by 4
- 2024Continuous Geometry-Aware Graph Diffusion via Hyperbolic Neural PDEcited by 2
- 2024Residual Hyperbolic Graph Convolution Networkscited by 2
- 2024Blind Deconvolution of Graph Signals: Robustness to Graph Perturbationscited by 1
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