# Community detection using fast low-cardinality semidefinite programming

arXiv: https://arxiv.org/abs/2012.02676 · HTML: https://mlsanity.com/paper/2012.02676/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Towards Faster Graph Partitioning via Pre-training and Inductive Inference](https://mlsanity.com/paper/2409.00670/) (2024)
- [InfraredGP: Efficient Graph Partitioning via Spectral Graph Neural Networks with Negative Corrections](https://mlsanity.com/paper/2508.19737/) (2025)
- [Graph clustering with Boltzmann machines](https://mlsanity.com/paper/2203.02471/) (2022)
- [Trading off Quality for Efficiency of Community Detection: An Inductive Method across Graphs](https://mlsanity.com/paper/2209.14825/) (2022)

## Abstract (arXiv)

Modularity maximization has been a fundamental tool for understanding the community structure of a network, but the underlying optimization problem is nonconvex and NP-hard to solve. State-of-the-art algorithms like the Louvain or Leiden methods focus on different heuristics to help escape local optima, but they still depend on a greedy step that moves node assignment locally and is prone to getting trapped. In this paper, we propose a new class of low-cardinality algorithm that generalizes the local update to maximize a semidefinite relaxation derived from max-k-cut. This proposed algorithm is scalable, empirically achieves the global semidefinite optimality for small cases, and outperforms the state-of-the-art algorithms in real-world datasets with little additional time cost. From the algorithmic perspective, it also opens a new avenue for scaling-up semidefinite programming when the solutions are sparse instead of low-rank.