Complex non-backtracking matrix for directed graphs
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Abstract (arXiv)
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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References · 11
- 2013Spectral redemption: clustering sparse networkscited by 56
- 2019Hermitian matrices for clustering directed graphs: insights and applicationscited by 27
- 2014Spectral Clustering of Graphs with the Bethe Hessiancited by 23
- 2020Higher-Order Spectral Clustering of Directed Graphscited by 17
- 2014Localization and centrality in networkscited by 7
- 2013Spectral community detection in sparse networkscited by 5
- 2022Skew-Symmetric Adjacency Matrices for Clustering Directed Graphscited by 4
- 2015A message-passing approach for recurrent-state epidemic models on networkscited by 3
- 2016Non-Backtracking Spectrum of Degree-Corrected Stochastic Block Modelscited by 3
- 2025An iterative spectral algorithm for digraph clusteringcited by 2
- 2016Leveraging percolation theory to single out influential spreaders in networkscited by 1
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