TL;DR
This paper develops new mathematical tools for hypergraph analysis, including gradient and Laplacian operators, enabling advanced modeling of dynamics and information flow in complex networks and image processing.
Contribution
It introduces novel gradient, adjoint, and $p$-Laplacian definitions for both oriented and unoriented hypergraphs, expanding the analytical framework.
Findings
Defined hypergraph gradient and Laplacian operators.
Applied these operators to model diffusion and flow in networks.
Demonstrated applications in social network dynamics and image processing.
Abstract
This paper introduces gradient, adjoint, and -Laplacian definitions for oriented hypergraphs as well as differential and averaging operators for unoriented hypergraphs. These definitions are used to define gradient flows in the form of diffusion equations with applications in modelling group dynamics and information flow in social networks as well as performing local and non-local image processing.
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