Complex non-backtracking matrix for directed graphs
This work addresses graph data analysis for researchers, but it appears incremental as it builds on existing matrix methods without major breakthroughs.
The paper tackles the problem of analyzing directed graphs by proposing a complex non-backtracking matrix that combines Hermitian adjacency and non-backtracking matrices, revealing relationships and insights for clustering in sparse directed graphs.
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.