提出复数非回溯矩阵，提升稀疏有向图聚类效果
Complex non-backtracking matrix for directed graphs
- 融合赫尔米特邻接矩阵与非回溯矩阵特性
- 在稀疏有向图上有效保留聚类信息
- 适合有向图结构分析与社区发现任务
图表示矩阵是图数据分析的核心工具。近期研究提出赫尔米特邻接矩阵以探索有向图结构，已有工作证明其在聚类中能提取有价值信息。本文提出复数非回溯矩阵，整合了赫尔米特邻接矩阵与非回溯矩阵的特性。该矩阵具有与无向图非回溯矩阵相似的性质。我们揭示了复数非回溯矩阵与赫尔米特邻接矩阵之间的关系，并提供了重要洞察：该矩阵表示在稀疏有向图中蕴含聚类信息。
原文摘要 · Abstract (English)
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.
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