A spectral method to incidence balance of oriented hypergraphs and induced signed hypergraphs

Abstract

An oriented hypergraph is a hypergraph together with an incidence orientation such that each edge-vertex incidence is given a label of $+1$ or $-1$. An oriented hypergraph is called incidence balanced if there exists a bipartition of the vertex set such that every edge intersects one part of the bipartition in positively incident vertices with the edge and other part in negatively incident vertices with the edge. In this paper, we investigate the incidence balance of oriented hypergraphs and induced signed hypergraphs by means of the eigenvalues of associated matrices and tensors, and provide a spectral method to characterize the incidence balanced oriented hypergraphs and their induced signed hypergraphs.

References in corpus (7)

• An Oriented Hypergraphic Approach to Algebraic Graph Theory
• Spectral Properties of Oriented Hypergraphs
• The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs
• Eigenvariety of Nonnegative Symmetric Weakly Irreducible Tensors Associated with Spectral Radius and Its Application to Hypergraphs
• The Signless Laplacian Matrix of Hypergraphs
• Eigenvectors of Laplacian or signless Laplacian of Hypergraphs Associated with Zero Eigenvalue
• Intersection Graphs of Oriented Hypergraphs and Their Matrices

Cited by in corpus (1)

• Incidence Hypergraphs: Box Products & the Laplacian