# Weighted Flow Diffusion for Local Graph Clustering with Node Attributes: an Algorithm and Statistical Guarantees

arXiv: https://arxiv.org/abs/2301.13187 · HTML: https://mlsanity.com/paper/2301.13187/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2023.

## Built on by (most cited first, 7 of 7)

- [Query-Aware Flow Diffusion for Graph-Based RAG with Retrieval Guarantees](https://mlsanity.com/paper/2605.18775/) (2026)
- [Local Clustering on Complex Graphs and Complex Hypergraphs](https://mlsanity.com/paper/2412.03008/) (2024)
- [DDiT: Dynamic Patch Scheduling for Efficient Diffusion Transformers](https://mlsanity.com/paper/2602.16968/) (2026)
- [Local Graph Clustering with Noisy Labels](https://mlsanity.com/paper/2310.08031/) (2023)
- [Adaptive Local Clustering over Attributed Graphs](https://mlsanity.com/paper/2503.20488/) (2025)
- [Cross-Domain Diffusion with Progressive Alignment for Efficient Adaptive Retrieval](https://mlsanity.com/paper/2505.13907/) (2025)
- [From Static Spectra to Operando Infrared Dynamics: Physics Informed Flow Modeling and a Benchmark](https://mlsanity.com/paper/2602.18551/) (2026)

## Abstract (arXiv)

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking and node embedding. While prior work on local graph clustering mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with node attributes that provide valuable additional information. We present a simple local graph clustering algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while accounting for both structural and attribute proximities. Using high-dimensional concentration results, we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster with a single seed node. We give conditions under which a target cluster generated from a fairly general contextual random graph model, which includes both the stochastic block model and the planted cluster model as special cases, can be fully recovered with bounded false positives. Empirically, we validate all theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior local clustering performances using real-world graph datasets.