A spectral method to incidence balance of oriented hypergraphs and induced signed hypergraphs. Issue 19 (16th December 2022)

• Record Type: Journal Article
• Authors: Wang, Yi; Le, Wang; Fan, Yi-Zheng
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 19(2022)
• Page Start: 4804
• Page End: 4818
• Publication Date: 2022-12-16
• Subjects: Oriented hypergraph -- signed hypergraph -- balance -- tensor -- eigenvalue; 05C65 -- 15A18; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1899110
• Languages: English
• ISSNs: 0308-1087

Abstract

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.