  The ranking of nodes in a network according to their ``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 is related to the selection of
which individuals should be tested in a population of asymptomatic individuals,
or which individuals should be vaccinated first. Motivated by the COVID-19
spreading dynamics, in this paper we review the most popular methods for node
ranking in undirected unweighted graphs, and compare their performance in a
benchmark realistic network, that takes into account the community-based
structure of society. Also, we generalize a classic benchmark network
originally proposed by Newman for ranking nodes in unweighted graphs, to show
how ranks change in the weighted case.
