# Detectability of the spectral method for sparse graph partitioning

arXiv: https://arxiv.org/abs/1509.06484 · HTML: https://mlsanity.com/paper/1509.06484/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [Consistency between ordering and clustering methods for graphs](https://mlsanity.com/paper/2208.12933/) (2022)

## Abstract (arXiv)

We show that modularity maximization with the resolution parameter offers a unifying framework of graph partitioning. In this framework, we demonstrate that the spectral method exhibits universal detectability, irrespective of the value of the resolution parameter, as long as the graph is partitioned. Furthermore, we show that when the resolution parameter is sufficiently small, a first-order phase transition occurs, resulting in the graph being unpartitioned.