A QUBO formulation for top-$\tau$ eigencentrality nodes

TL;DR

This paper introduces a QUBO-based approach to identify top-$ au$ eigencentrality nodes in networks using quantum computing, enabling efficient ranking of node importance on quantum hardware.

Contribution

It formulates the top-$ au$ eigencentrality node ranking problem as a QUBO, facilitating quantum solutions on D-Wave and IBM quantum computers.

Findings

Successfully identified top-$ au$ eigencentrality nodes in various networks.

Demonstrated feasibility of quantum algorithms for centrality ranking.

Provided a new quantum formulation for network analysis tasks.

Abstract

The efficient calculation of the centrality or "hierarchy" of nodes in a network has gained great relevance in recent years due to the generation of large amounts of data. The eigenvector centrality (aka eigencentrality) is quickly becoming a good metric for centrality due to both its simplicity and fidelity. In this work we lay the foundations for solving the eigencentrality problem of ranking the importance of the nodes of a network with scores from the eigenvector of the network, using quantum computational paradigms such as quantum annealing and gate-based quantum computing. The problem is reformulated as a quadratic unconstrained binary optimization (QUBO) that can be solved on both quantum architectures. The results focus on correctly identifying a given number of the most important nodes in numerous networks given by the sparse vector solution of our QUBO formulation of the problem of identifying the top-$\tau$ highest eigencentrality nodes in a network on both the D-Wave and IBM quantum computers