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 current COVID-19 pandemic has recently rejuvenated the interest in this problem, as it informs the selection of which individuals should be tested in a population of asymptomatic individuals, or which individuals should be vaccinated first. Motivated by these issues, in this paper we review some popular methods for node ranking in undirected unweighted graphs, and compare their performance in a benchmark realistic network that takes into account the communitybased structure of society. In particular, we use the information of the relevance of individuals in the network to take a control decision, i.e., which individuals should be tested, and possibly quarantined. Finally, we also review the extension of these ranking methods to weighted graphs, and explore the importance of weights in a contact network by exhibiting a toy model and comparing node rankings for this case in the context of disease spread