  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.
