  Clustering nodes in heterophilous graphs presents unique challenges due to
the asymmetric relationships often overlooked by traditional methods, which
moreover assume that good clustering corresponds to high intra-cluster and low
inter-cluster connectivity. To address these issues, we introduce HeNCler - a
novel approach for Heterophilous Node Clustering. Our method begins by defining
a weighted kernel singular value decomposition to create an asymmetric
similarity graph, applicable to both directed and undirected graphs. We further
establish that the dual problem of this formulation aligns with asymmetric
kernel spectral clustering, interpreting learned graph similarities without
relying on homophily. We demonstrate the ability to solve the primal problem
directly, circumventing the computational difficulties of the dual approach.
Experimental evidence confirms that HeNCler significantly enhances performance
in node clustering tasks within heterophilous graph contexts.
