On node ranking in graphs

TL;DR

This paper reviews and compares popular node ranking methods in undirected unweighted graphs, motivated by COVID-19, and extends a benchmark to weighted graphs to analyze how rankings vary.

Contribution

It provides a comprehensive review and performance comparison of node ranking methods and generalizes a benchmark for weighted graphs, addressing COVID-19 related network analysis.

Findings

Performance varies across different network structures

Weighted rankings differ significantly from unweighted cases

Benchmark results highlight strengths and weaknesses of methods

Abstract

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.