# Sampling on networks: estimating eigenvector centrality on incomplete graphs

## TL;DR

This paper introduces a novel sampling method for accurately estimating eigenvector centrality in incomplete networks, addressing challenges of limited data and large-scale graphs with improved reliability over traditional approaches.

## Contribution

The authors propose a spectral approximation-based sampling algorithm that enhances eigenvector centrality estimation on incomplete networks, outperforming traditional methods like random walk and uniform sampling.

## Key findings

- The new method provides more reliable eigenvector centrality estimates.
- It maintains computational scalability for large networks.
- Performance improvements are demonstrated on both synthetic and real data.

## Abstract

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios where data collection is expensive, the network is too big for data storage capacity or only partial information is available. The sampling algorithm is theoretically grounded by results derived from spectral approximation theory. We studied the problem on both synthetic and real data and tested the performance comparing with traditional methods, such as random walk and uniform sampling. We show that approximations obtained from such methods are not always reliable and that our algorithm, while preserving computational scalability, improves performance under different error measures.