On node ranking in graphs

Ekaterina Dudkina, Michelangelo Bin, Jane Breen, Emanuele Crisostomi, Pietro Ferraro, Steve Kirkland, Jakub Marecek, Roderick Murray-Smith, Thomas Parisini, Lewi Stone, Serife Yilmaz, Robert Shorten

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.

Knowledge Graph

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