In this paper, we study bearing equivalence in directed graphs. We first give a strengthened definition of bearing equivalence based on the \textit{kernel equivalence} relationship between bearing rigidity matrix and bearing Laplacian matrix. We then present several conditions to characterize bearing equivalence for both directed acyclic and cyclic graphs. These conditions involve the spectrum and null space of the associated bearing Laplacian matrix for a directed bearing formation. For directed acyclic graphs, all eigenvalues of the associated bearing Laplacian are real and nonnegative, while for directed graphs containing cycles, the bearing Laplacian can have eigenvalues with negative real parts. Several examples of bearing equivalent and bearing non-equivalent formations are given to illustrate these conditions.

翻译：在本文中,我们研究方向图中的等值。 我们首先根据刻度矩阵与拉普拉西亚矩阵之间的关系,给出一个更强的等值定义。 然后我们提出若干条件,说明定向环状图和环形图的等值。 这些条件涉及相关带拉普拉西亚矩阵的频谱和无空空间,用于定向轴承形成。 对于定向环形图,相关带拉普拉西亚的所有等值都是真实的和非负的,而对于含有周期的定向图,带拉普拉西亚的可具有负真实部分的等值。 提供了若干具有等值和带非等值结构的例子,以说明这些条件。</s>