# Eigenvector localization in real networks and its implications for epidemic spreading

arXiv: https://arxiv.org/abs/1801.05649 · HTML: https://mlsanity.com/paper/1801.05649/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2018.

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

- [Stratified Graph Spectra](https://mlsanity.com/paper/2201.03696/) (2022)

## Abstract (arXiv)

The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization properties of the principal eigenvector in real networks. We show that in most cases it is either localized on the star defined by the node with largest degree (hub) and its nearest neighbors, or on the densely connected subgraph defined by the maximum K-core in a K-core decomposition. The localization of the principal eigenvector is often strongly correlated with the value of the largest eigenvalue, which is given by the local eigenvalue of the corresponding localization subgraph, but different scenarios sometimes occur. We additionally show that simple targeted immunization strategies for epidemic spreading are extremely sensitive to the actual localization set.