Numerical Investigation of Metrics for Epidemic Processes on Graphs

TL;DR

This paper introduces the epidemic hitting time (EHT) metric to quantify epidemic spread on graphs, compares it with existing centrality measures, and reveals its high correlation with effective resistance and its delocalized nature.

Contribution

The study develops the EHT metric for epidemic propagation, providing new insights into node importance and spreading dynamics on networks.

Findings

EHT centrality correlates highly with effective resistance centrality.

EHT centrality is more delocalized than degree and spectral centrality.

Peripheral nodes play a significant role in epidemic spreading.

Abstract

This study develops the epidemic hitting time (EHT) metric on graphs measuring the expected time an epidemic starting at node $a$ in a fully susceptible network takes to propagate and reach node $b$. An associated EHT centrality measure is then compared to degree, betweenness, spectral, and effective resistance centrality measures through exhaustive numerical simulations on several real-world network data-sets. We find two surprising observations: first, EHT centrality is highly correlated with effective resistance centrality; second, the EHT centrality measure is much more delocalized compared to degree and spectral centrality, highlighting the role of peripheral nodes in epidemic spreading on graphs.