# Capacity Releasing Diffusion for Speed and Locality

arXiv: https://arxiv.org/abs/1706.05826 · HTML: https://mlsanity.com/paper/1706.05826/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2017.

## Built on by (most cited first, 10 of 10)

- [Annealed Training for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2207.11542/) (2022)
- [Local Hyper-Flow Diffusion](https://mlsanity.com/paper/2102.07945/) (2021)
- [Query-Aware Flow Diffusion for Graph-Based RAG with Retrieval Guarantees](https://mlsanity.com/paper/2605.18775/) (2026)
- [Local Algorithms for Finding Densely Connected Clusters](https://mlsanity.com/paper/2106.05245/) (2021)
- [A Compressed Sensing Based Least Squares Approach to Semi-supervised Local Cluster Extraction](https://mlsanity.com/paper/2202.02904/) (2022)
- [Graph-based Semi-supervised Local Clustering with Few Labeled Nodes](https://mlsanity.com/paper/2211.11114/) (2022)
- [Scalable and Effective Conductance-based Graph Clustering](https://mlsanity.com/paper/2211.12511/) (2022)
- [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)
- [ℓ2-norm Flow Diffusion in Near-Linear Time](https://mlsanity.com/paper/2105.14629/) (2021)

## Abstract (arXiv)

Diffusions and related random walk procedures are of central importance in many areas of machine learning, data analysis, and applied mathematics. Because they spread mass agnostically at each step in an iterative manner, they can sometimes spread mass "too aggressively," thereby failing to find the "right" clusters. We introduce a novel Capacity Releasing Diffusion (CRD) Process, which is both faster and stays more local than the classical spectral diffusion process. As an application, we use our CRD Process to develop an improved local algorithm for graph clustering. Our local graph clustering method can find local clusters in a model of clustering where one begins the CRD Process in a cluster whose vertices are connected better internally than externally by an O(log2 n) factor, where n is the number of nodes in the cluster. Thus, our CRD Process is the first local graph clustering algorithm that is not subject to the well-known quadratic Cheeger barrier. Our result requires a certain smoothness condition, which we expect to be an artifact of our analysis. Our empirical evaluation demonstrates improved results, in particular for realistic social graphs where there are moderately good---but not very good---clusters.