$p$-Laplace Operators for Oriented 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 $p\ge 1$. Several spectral properties of these operators are investigated.

Vietnam Journal of Mathematics, To appear (2022)

References in corpus (7)

• Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
• Spectral Theory of Laplace Operators on Oriented Hypergraphs
• $p$-Laplace Operators for Oriented Hypergraphs
• Signless Normalized Laplacian for Hypergraphs
• Tight Continuous Relaxation of the Balanced $k$-Cut Problem
• Sharp bounds for the largest eigenvalue
• Cheeger-like inequalities for the largest eigenvalue of the graph Laplace Operator

Cited by in corpus (2)

• $p$-Laplace Operators for Oriented Hypergraphs
• Hypergraph $p$-Laplacians and Scale Spaces