Repelling curvature via $ε-$repelling Laplacian on positive connected signed graphs

[2506.10492] Repelling curvature via $ε-$repelling Laplacian on positive connected signed graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Spectral Theory arXiv:2506.10492 (math) [Submitted on 12 Jun 2025] Title: Repelling curvature via $ε-$repelling Laplacian on positive connected signed graphs Authors: Yong Lin , Shi Wan View a PDF of the paper titled Repelling curvature via $\epsilon-$repelling Laplacian on positive connected signed graphs, by Yong Lin and Shi Wan View PDF HTML (experimental) Abstract: The paper defines a positive semidefinite operator called $\epsilon-$repelling Laplacian on a positive connected signed graph where $\epsilon$ is an arbitrary positive number less than a constant $\epsilon_0$ related to the graph's consensus problem. Then we investigate the upper bound of the second smallest eigenvalue of $\epsilon-$repelling Laplacian. Besides, we use the pseudoinverse of $\epsilon-$repelling Laplacian to construct a simplex as well as $\epsilon-$repelling cost whose square root turns out to be a distance among the vertices of the simplex. We also extend the node and edge resistance curvature proposed by this http URL et al. to node and edge $\epsilon-$repelling curvature and derive the corresponding Lichnerowicz inequalities on any positive connected signed graph. Moreover, it turns out that edge $\epsilon-$repelling curvature is no more than the Lin-Lu-Yau curvature of the underlying graph whose transport cost is $\epsilon-$repelling cost rather than the length of the shortest path. Subjects: Spectral Theory (math.SP) Cite as: arXiv:2506.10492 [math.SP] (or arXiv:2506.10492v1 [math.SP] for this version) https://doi.org/10.48550/arXiv.2506.10492 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s12220-026-02420-1 Focus to learn more DOI(s) linking to related resources Submission history From: Shi Wan [ view email ] [v1] Thu, 12 Jun 2025 08:49:45 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled Repelling curvature via $\epsilon-$repelling Laplacian on positive connected signed graphs, by Yong Lin and Shi Wan View PDF HTML (experimental) TeX Source view license Current browse context: math.SP < prev | next > new | recent | 2025-06 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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