Many real networks are inherently directed: messages, goods and money flow in specific directions, and this orientation carries crucial structural information. This thesis revisits five adjacency–based spectral clustering algorithms for directed graphs: Adjacency Spectral Embedding (ASE), Hermitian (HERM), Skew–symmetric (SKEW), Block–Cyclic (BCS) and Block–Acyclic (BAS). We provide a study on a modification of these algorithms: before k-means, the spectral coordinates are reduced to two dimensions using t-SNE, leading to an improvement of the final clustering. The spectral core of each method is left unchanged. The analysis covers the considered algorithms, implementation details, and complexity analyses. In the dense regime all spectral variants are dominated by the O(n3) cost of the eigen/SVD step with O(n2) memory, whereas the added Barnes–Hut t-SNE contributes only O(n log n) and does not alter the asymptotic bottleneck. Performance is evaluated on synthetic and real graphs using both label–based metrics (NMI, F-Score, ARI) and either directionality-aware, or flow-based criteria (Cut–Imbalance and Trade–Flow). Directed Stochastic Block Models (DSBMs) show that the refinement consistently reduces the errors in the classification across a wide range of community counts. LFR benchmarks indicate that the gain persists under substantial inter–community mixing. On real-world datasets emerging from e-mail communications and banking transactions, the refined pipelines yield more interpretable clusters and improved flow structure between them. Overall, a geometric adjustment applied after the eigenspectrum analysis step reliably tightens same–community neighborhoods without changing the dominant computational cost. The result is a unified, implementation– ready toolkit for clustering directed graphs that improves empirical separability while preserving the theoretical and algorithmic foundations of the underlying spectral methods.
