A comparison of centrality measures and their role in controlling the spread in epidemic networks

The ranking of nodes in a network according to their centrality or ``importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread.