# Exact Recovery by Neighborhood Smoothing in Directed Stochastic Block Models

arXiv: https://arxiv.org/abs/2601.16427 · HTML: https://mlsanity.com/paper/2601.16427/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2026.

## Abstract (arXiv)

We study exact community recovery in sparse directed stochastic block models using neighborhood smoothing of connection-probability profiles. The proposed method clusters vertices according to their estimated outgoing connection-probability profiles. For each vertex, its complete outgoing profile is estimated by averaging the adjacency rows of empirically similar vertices, after which (K)-means is applied to the estimated profiles. An analogous procedure based on incoming connection-probability profiles is obtained by applying the same construction to the transposed adjacency matrix. We establish a finite-sample uniform row-wise error bound for the asymmetric smoothed estimator and derive consistency in the normalized two-to-infinity norm. We then show that exact recovery follows when the minimum separation between distinct population profiles dominates the row-wise estimation error. The result permits a vanishing sparsity factor, a general asymmetric block-probability matrix, and a number of communities that may diverge with the network size. We are unaware of a previous exact-recovery theorem that simultaneously covers these features for a directed stochastic block model. Numerical studies and an application to a directed neuronal connectome illustrate the practical behavior and limitations of the profile-based clustering approach.