Hypergraph p-Laplacians, Scale Spaces, and Information Flow in Networks
Fazeny A, Tenbrinck D, Burger M (2023)
Publication Type: Conference contribution
Publication year: 2023
Journal
Original Authors: Ariane Fazeny, Daniel Tenbrinck, Martin Burger
Series: SSVM 2023: Scale Space and Variational Methods in Computer Vision
Pages Range: 677-690
Conference Proceedings Title: SSVM 2023: Scale Space and Variational Methods in Computer Vision
Event location: Santa Margherita di Pula
ISBN: 9783031319747
DOI: 10.1007/978-3-031-31975-4_52
Abstract
The aim of this paper is to revisit the definition of differential operators on hypergraphs, which are a natural extension of graphs in systems based on interactions beyond pairs. In particular we focus on the definition of Laplacian and p-Laplace operators, their basic spectral properties, variational structure, and their scale spaces.
We shall see that the corresponding gradient flows, i.e., diffusion equations on hypergraphs, are possible models for the information flow on social networks, e.g., in opinion formation based on group discussion. Moreover, the spectral analysis and scale spaces induced by these operators provide a potential method to further analyze complex networks and their multiscale structure.
The quest for spectral analysis on hypergraphs motivates in particular a definition of differential operators with trivial first eigenfunction and thus more interpretable second eigenfunctions. This property is not automatically satisfied in existing definitions of hypergraph p-Laplacians and we hence provide a novel axiomatic approach that extends previous definitions and can be specialized to satisfy such (or other) desired properties.
Authors with CRIS profile
Ariane Fazeny
Sonderforschungsbereich/Transregio 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken
Daniel Tenbrinck
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
Martin Burger
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)
How to cite
APA:
Fazeny, A., Tenbrinck, D., & Burger, M. (2023). Hypergraph p-Laplacians, Scale Spaces, and Information Flow in Networks. In SSVM 2023: Scale Space and Variational Methods in Computer Vision (pp. 677-690). Santa Margherita di Pula, IT.
MLA:
Fazeny, Ariane, Daniel Tenbrinck, and Martin Burger. "Hypergraph p-Laplacians, Scale Spaces, and Information Flow in Networks." Proceedings of the International Conference on Scale Space and Variational Methods in Computer Vision, Santa Margherita di Pula 2023. 677-690.
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