Estimating noncommutative distances on graphs

2021/05/19 by Fabien Besnard, Besnard, Fabien · 1 citation
Mathematics · Physics and Astronomy · #05C99 #58B34 #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.CO #math.OA #msc:05C99 #msc:58B34

paper · pdf · doi:10.48550/arxiv.2105.09056

24 p, 4 figures. Comments welcome !

arxiv created 2021/05/19 · openalex publication_date 2021/05/19 · arxiv updated 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We report on some findings concerning Connes' noncommutative distance d on a weighted undirected graph G. Our main result is the lower bound ℓ/Δ(G)≤ d where ℓ is the geodesic distance and Δ(G) the degree of G. It is obtained thanks to an auxiliary spectral triple on the collection of the edges of G.

Citations

• Connes' Distance Function on One-Dimensional Lattices

Cited by

• Geometric Features of Higher-Order Networks via the Spectral Triplet

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