# Localization and centrality in networks

arXiv: https://arxiv.org/abs/1401.5093 · HTML: https://mlsanity.com/paper/1401.5093/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2014.

## Built on by (most cited first, 7 of 7)

- [Nonbacktracking spectral clustering of nonuniform hypergraphs](https://mlsanity.com/paper/2204.13586/) (2022)
- [Faster Local Solvers for Graph Diffusion Equations](https://mlsanity.com/paper/2410.21634/) (2024)
- [Critical Nodes Identification in Complex Networks: A Survey](https://mlsanity.com/paper/2507.06164/) (2025)
- [A Network Science perspective of Graph Convolutional Networks: A survey](https://mlsanity.com/paper/2301.04824/) (2023)
- [Thematic recommendations on knowledge graphs using multilayer networks](https://mlsanity.com/paper/2105.05733/) (2021)
- [Identifying Influential Nodes in Two-mode Data Networks using Formal Concept Analysis](https://mlsanity.com/paper/2109.03372/) (2021)
- [Complex non-backtracking matrix for directed graphs](https://mlsanity.com/paper/2507.12503/) (2025)

## Abstract (arXiv)

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired. As a remedy, we propose an alternative centrality measure based on the nonbacktracking matrix, which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved, but avoids localization and gives useful results in regimes where the standard centrality fails.