# Localized eigenvectors of the non-backtracking matrix

arXiv: https://arxiv.org/abs/1505.07543 · HTML: https://mlsanity.com/paper/1505.07543/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2015.

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

- [Stationary distribution of node2vec random walks on household models](https://mlsanity.com/paper/2502.19039/) (2025)

## Abstract (arXiv)

In the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical experiments on several examples of real networks, it is clear that the non-backtracking matrix does not exhibit localization of eigenvectors. However, we show that localized eigenvectors of the non-backtracking matrix can exist outside the spectral band, which may lead to deterioration in the performance of graph partitioning.