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

• URL: http://arxiv.org/abs/2506.15464v1
• Date: Wed, 18 Jun 2025 13:55:30 GMT
• Title: Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs
• Authors: Le Vu Anh, Mehmet Dik, Nguyen Viet Anh,
• Abstract summary: Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters.<n>We introduce a boundary-weighted operator that rescales each edge according to how far its endpoints drift toward the graph's Gromov boundary.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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