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.

中文翻译：

---

定向超图和诱导符号超图的入射平衡的光谱方法

摘要

如果每个边缘-顶点入射都具有标记，则称超图是定向的 $+\mathrm{1个}$ 或者 $-\mathrm{1个}$。如果存在顶点集的等分线，使得每个边在正入射顶点与边相交，而另一部分在负入射顶点与边相交，则定向超图被称为入射平衡。在本文中，我们通过关联矩阵和张量的特征值研究定向超图和诱导签名超图的发生率平衡，并提供一种频谱方法来表征入射平衡的定向超图及其诱导签名超图。