Clustering nodes in heterophilous graphs is challenging as traditional methods assume that effective clustering is characterized by high intra-cluster and low inter-cluster connectivity. To address this, we introduce HeNCler—a novel approach for Heterophilous Node Clustering. HeNCler learns a similarity graph by optimizing a clustering-specific objective based on weighted kernel singular value decomposition Our approach enables spectral clustering on an asymmetric similarity graph, providing flexibility for both directed and undirected graphs. By solving the primal problem directly, our method overcomes the computational difficulties of traditional adjacency partitioning-based approaches. Experimental results show that HeNCler significantly improves node clustering performance in heterophilous graph settings, highlighting the advantage of its asymmetric graph-learning framework.