Search for: All records

Recent spectral graph sparsificationresearch aims to construct ultra-sparse subgraphs for preserving the original graph spectral (structural) properties, such as the first few Laplacian eigenvalues and eigenvectors, which has led to the development of a variety of nearly linear time numerical and graph algorithms. However, there is very limited progress in the spectral sparsification of directed graphs. In this work, we prove the existence of nearly linear-sized spectral sparsifiers for directed graphs under certain conditions. Furthermore, we introduce a practically efficient spectral algorithm (diGRASS) for sparsifying real-world, large-scale directed graphs leveraging spectral matrix perturbation analysis. The proposed method has been evaluated using a variety of directed graphs obtained from real-world applications, showing promising results for solving directed graph Laplacians, spectral partitioning of directed graphs, and approximately computing (personalized) PageRank vectors.