Thus far, digraphs that are uniquely determined by their Hermitian spectra have proven elusive. Instead, researchers have turned to spectral determination of classes of switching equivalent digraphs, rather than individual digraphs. In the present paper, we consider the traditional notion: a digraph (or mixed graph) is said to be strongly determined by its Hermitian spectrum (abbreviated SHDS) if it is isomorphic to each digraph to which it is cospectral. Convincing numerical evidence to support the claim that this property is extremely rare is provided. Nonetheless, the first infinite family of connected digraphs that is SHDS is constructed. This family is obtained via the introduction of twin vertices into a structure that is named negative tetrahedron. This special digraph, that exhibits extreme spectral behavior, is contained in the surprisingly small collection of all digraphs with exactly one negative eigenvalue, which is determined as an intermediate result.

到目前为止，已证明由其厄米光谱唯一确定的二合图。取而代之的是，研究人员已转向切换等效图的类别而不是单个图的频谱确定。在本文中，我们考虑了传统概念：如果有向图的每个有向图是同构的，则有向图（或混合图）据说是由其Hermitian光谱（缩写为SHDS）强烈确定的。提供了令人信服的数字证据来支持该属性极为罕见的说法。尽管如此，仍然构造了第一个无穷大的连通有向图，即SHDS。该族是通过将双顶点引入称为负四面体的结构而获得的。这种特殊的有向图，表现出极端的光谱行为，被包含在所有带有正负本征值的有向图的极小集合中，这被确定为中间结果。