$p$-Laplace Operators for Oriented Hypergraphs

TL;DR

This paper generalizes the $p$-Laplacian to oriented hypergraphs, defining vertex and hyperedge $p$-Laplacians for all $p \,\geq\, 1$, and explores their spectral properties.

Contribution

It introduces new $p$-Laplacian operators for oriented hypergraphs, extending existing graph Laplacians to a more general hypergraph setting.

Findings

Defined vertex and hyperedge $p$-Laplacians for all $p\geq 1$

Investigated spectral properties of these operators

Extended classical Laplacian concepts to hypergraphs

Abstract

The $p$-Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particular, both a vertex $p$-Laplacian and a hyperedge $p$-Laplacian are defined for oriented hypergraphs, for all $p\geq 1$. Several spectral properties of these operators are investigated.