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

ABSTRACT

A hypergraph is said to be oriented if each edge-vertex incidence has 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 the 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.

Keywords:

• Oriented hypergraph
• signed hypergraph
• balance
• tensor
• eigenvalue

2010 Mathematics Subject Classifications:

• 05C65
• 15A18

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11771016], [grant number 11871073].