论文标题
图形光谱中定向性的贡献
Contribution of directedness in graph spectra
论文作者
论文摘要
在图形分析中，有向边的边缘通常近似于无方向性的边缘，以使邻接矩阵可能是对称的。但是，这种简化尚未得到彻底验证。在这项研究中，我们通过引入随机指导来研究定向性如何影响图光谱，这是忽略边缘方向的相反操作。我们分析表明，统一的随机指导通常会保存扰动状态中邻接矩阵的相对频谱结构。随机指导的结果意味着在忽略了定向性后可以保守邻接矩阵的光谱。
In graph analyses, directed edges are often approximated to undirected ones so that the adjacency matrices may be symmetric. However, such simplification has not been thoroughly verified. In this study, we investigate how directedness affects the graph spectra by introducing random directization, which is an opposite operation of neglecting edge directions. We analytically reveal that uniformly random directization typically conserves the relative spectral structure of the adjacency matrix in the perturbative regime. The result of random directization implies that the spectrum of the adjacency matrix can be conserved after the directedness is ignored.
