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 is quickly becoming a good metric for centrality due to both its simplicity and fidelity. In this work we lay the foundations for the calculation of eigenvector centrality 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 our QUBO formulation of eigenvector centrality on both the D-Wave and IBM quantum computers.
A QUBO Formulation for Eigencentrality