Fast Estimation of Percolation Centrality

TL;DR

This paper introduces a fast, randomized algorithm for approximating percolation centrality in networks, providing probabilistic guarantees and demonstrating improved speed and accuracy over existing methods through extensive experiments.

Contribution

The paper presents a novel randomized approximation algorithm for percolation centrality with theoretical guarantees, extending techniques from betweenness centrality estimation.

Findings

Algorithm achieves high-quality estimates within $ ext{ε}$ with probability at least $1- ext{δ}$.

Experimental results show improved speed and reduced sample size compared to previous methods.

Maintains high accuracy of centrality estimates on real-world networks.

Abstract

In this work, we present a new algorithm to approximate the percolation centrality of every node in a graph. Such a centrality measure quantifies the importance of the vertices in a network during a contagious process. In this paper, we present a randomized approximation algorithm that can compute probabilistically guaranteed high-quality percolation centrality estimates, generalizing techniques used by Pellegrina and Vandin (TKDD 2024) for the betweenness centrality. The estimation obtained by our algorithm is within $\varepsilon$ of the value with probability at least $1-\delta$, for fixed constants $\varepsilon,\delta \in (0,1)$. We our theoretical results with an extensive experimental analysis on several real-world networks and provide empirical evidence that our algorithm improves the current state of the art in speed, and sample size while maintaining high accuracy of the percolation centrality estimates.