Quantum hub and authority centrality measures for directed networks based on continuous-time quantum walks

TL;DR

This paper introduces three novel quantum algorithms based on continuous-time quantum walks for computing hub and authority centrality in directed networks, demonstrating their effectiveness and comparing them with classical methods.

Contribution

The paper presents three new quantum algorithms for centrality measures in directed networks, utilizing continuous-time quantum walks and bipartite graph constructions, with comprehensive testing and comparison.

Findings

CQAw is the most reliable method among the three.

Quantum methods produce rankings compatible with classical algorithms.

CQAu and CQG show unique features and potential applications.

Abstract

In this work we introduce, test and discuss three quantum methods for computing hub and authority centrality scores in directed networks. The methods are based on unitary, continuous-time quantum walks; the construction of a suitable Hermitian Hamiltonian is achieved by performing a quantum walk on the associated bipartite graph. Two methods, called CQAu and CQAw, use the same evolution operator, inspired by the classical HITS algorithm, but with different initial states; the computation of hub and authority scores is performed simultaneously. The third method, called CQG and inspired by classical PageRank, requires instead two separate runs with different evolution operators, one for hub and one for authority scores. The methods are tested on several directed graphs with different sizes and properties; a comparison with other well-established ranking algorithms is provided. CQAw emerges as the most reliable of the three methods and yields rankings that are largely compatible with results from HITS, although CQAu and CQG also present interesting features and potential for applications.