Abstract
We study network centrality measures that take into account the specific structure of networks with time-stamped edges. In particular, we explore how such measures can be used to identify nodes most relevant for the spread of epidemics on directed, temporal contact networks. We present a percolation study on the French cattle trade network, proving that time-aware centrality measures such as the TempoRank significantly outperform measures defined on the static network. In order to make TempoRank amenable to large-scale networks, we show how it can be efficiently computed through direct simulation of time-respecting random walks.
Highlights
When dealing with epidemic processes spreading along the edges of networks, centrality measures can be used to identify the nodes most important for disease transmission
We show that our stochastic method is able to compute TempoRank centrality measures on the large Base de Données Nationale d’Identification (BDNI) network, and, using a numerical percolation study, that they outperform static centrality measures in mitigating outbreak sizes
We see that the temporal centrality measures significantly outperform the static measures on the reconstructed network, which shows that temporal information plays a major part in the spread of infection on cattle trade networks, once its strong connectivity properties have been muted
Summary
When dealing with epidemic processes spreading along the edges of networks, centrality measures can be used to identify the nodes most important for disease transmission. Most approaches have focused on (temporal) path-counting methods, such as the Disease-Flow centralities in Natale et al (2009), closely related to the outgoing and ingoing contact chains described in Nöremark et al (2011) Such methods have proved useful in identifying epidemiologically important nodes (Büttner et al 2013; Vidondo and Voelkl 2018) but fail for large-scale networks due to combinatorial explosion in the number of nodes or the number of time-steps. Most centrality measures have moderately high overlap, with the exception of the TempoRank measure, which has low overlap with all other centralities The latter is probably due to it highly ranking vertices with no or few outgoing edges, on which random walkers spend a disproportionate amount of time, thereby increasing their TempoRank score. In cattle trade networks, markets and assembly centres act as trade hubs (Hoscheit et al 2017; Natale et al 2009; Bajardi et al 2011; Salines et al 2017)
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