# Differential Privacy from Locally Adjustable Graph Algorithms: k-Core Decomposition, Low Out-Degree Ordering, and Densest Subgraphs

arXiv: https://arxiv.org/abs/2211.10887 · HTML: https://mlsanity.com/paper/2211.10887/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2022.

## Built on by (most cited first, 6 of 6)

- [A Survey on the Densest Subgraph Problem and Its Variants](https://mlsanity.com/paper/2303.14467/) (2023)
- [Privacy-Preserving Graph Embedding based on Local Differential Privacy](https://mlsanity.com/paper/2310.11060/) (2023)
- [Communication Cost Reduction for Subgraph Counting under Local Differential Privacy via Hash Functions](https://mlsanity.com/paper/2312.07055/) (2023)
- [Differentially Private and Scalable Estimation of the Network Principal Component](https://mlsanity.com/paper/2505.03858/) (2025)
- [Continual Release of Densest Subgraphs: Privacy Amplification & Sublinear Space via Subsampling](https://mlsanity.com/paper/2510.11640/) (2025)
- [Differentially Private Modeling of Disease Transmission within Human Contact Networks](https://mlsanity.com/paper/2604.07493/) (2026)

## Abstract (arXiv)

Differentially private algorithms allow large-scale data analytics while preserving user privacy. Designing such algorithms for graph data is gaining importance with the growth of large networks that model various (sensitive) relationships between individuals. While there exists a rich history of important literature in this space, to the best of our knowledge, no results formalize a relationship between certain parallel and distributed graph algorithms and differentially private graph analysis. In this paper, we define locally adjustable graph algorithms and show that algorithms of this type can be transformed into differentially private algorithms. Our formalization is motivated by a set of results that we present in the central and local models of differential privacy for a number of problems, including k-core decomposition, low out-degree ordering, and densest subgraphs. First, we design an varepsilon-edge differentially private (DP) algorithm that returns a subset of nodes that induce a subgraph of density at least fracD^*1+η - Oleft(poly(log n)/varepsilonright), where D^* is the density of the densest subgraph in the input graph (for any constant η > 0). This algorithm achieves a two-fold improvement on the multiplicative approximation factor of the previously best-known private densest subgraph algorithms while maintaining a near-linear runtime. Then, we present an varepsilon-locally edge differentially private (LEDP) algorithm for k-core decompositions. Our LEDP algorithm provides approximates the core numbers (for any constant η > 0) with (2+η) multiplicative and Oleft(polyleft(log nright)/varepsilonright) additive error. This is the first differentially private algorithm that outputs private k-core decomposition statistics.