Nonlinear Modified PageRank Problem for Local Graph Partitioning
<|reference_start|>Nonlinear Modified PageRank Problem for Local Graph Partitioning: A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of the incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a strategy for obtaining a numerical solution to the generalised problem. Sets of vertices are formed according to the ranking supplied by the solution, and a conductance criterion decides upon the set that best represents the cluster around a starting vertex. Experiments on both synthetic and real-world inspired graphs demonstrate the capability of the approach to not only produce low conductance sets, but to also recover local clusters with an accuracy that consistently surpasses state-of-the-art algorithms.<|reference_end|>
@article{kodsi2024nonlinear,
    title={Nonlinear Modified PageRank Problem for Local Graph Partitioning},
    author={Costy Kodsi and Dimosthenis Pasadakis},
    journal={arXiv preprint arXiv:2409.01834},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01834},
    primaryClass={math.NA cs.NA}
}