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arXiv · 2603.11060

LLY Ricci Reweighting in Stochastic Block Models: Uniform Curvature Concentration and Finite-Horizon Tracking

Varun Kotharkar
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Abstract

We study curvature-driven edge reweighting for community recovery in the balanced two-block stochastic block model. Given a graph G with initial weights equal to the adjacency matrix, we iteratively update edge weights using Lin-Lu-Yau (Ollivier-type) Ricci curvature, while all transportation costs are computed in the unweighted graph metric. In a moderate-density regime we prove uniform concentration of edge curvatures and show that a single Ricci reweighting step produces a two-level weighting that amplifies within-block connectivity relative to across-block connectivity. As a consequence, spectral clustering on the reweighted graph has a strictly larger population eigengap, and we obtain corresponding non-asymptotic perturbation bounds and Davis-Kahan misclustering guarantees. We further analyze a fixed finite horizon of iterated reweighting, where the random iterates track a deterministic two-weight recursion uniformly over the time horizon. This yields a principled finite-horizon curvature flow interpretation for community detection in a canonical random graph model.

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Varun Kotharkar. 2026-03-04. LLY Ricci Reweighting in Stochastic Block Models: Uniform Curvature Concentration and Finite-Horizon Tracking. https://arxiv.org/abs/2603.11060

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