标题： 有向图的复数非回溯矩阵 显示英文标题

标题： Complex non-backtracking matrix for directed graphs

摘要： 图表示矩阵是图数据分析中的重要工具。 最近，提出了埃尔米特邻接矩阵来研究有向图结构。 以前的研究表明，这些矩阵可以提取用于聚类的有价值信息。 在本文中，我们提出了复数非回溯矩阵，该矩阵结合了埃尔米特邻接矩阵和非回溯矩阵的特性。 所提出的矩阵与无向图的非回溯矩阵具有相似的性质。 我们揭示了复数非回溯矩阵与埃尔米特邻接矩阵之间的关系。 此外，我们提供了有趣的见解，表明这种矩阵表示包含聚类信息，特别是对于稀疏有向图。 显示英文摘要

摘要： Graph representation matrices are essential tools in graph data analysis. Recently, Hermitian adjacency matrices have been proposed to investigate directed graph structures. Previous studies have demonstrated that these matrices can extract valuable information for clustering. In this paper, we propose the complex non-backtracking matrix that integrates the properties of the Hermitian adjacency matrix and the non-backtracking matrix. The proposed matrix has similar properties with the non-backtracking matrix of undirected graphs. We reveal relationships between the complex non-backtracking matrix and the Hermitian adjacency matrix. Also, we provide intriguing insights that this matrix representation holds cluster information, particularly for sparse directed graphs.