Identifying key players in complex networks via network entanglement

Empirical networks exhibit significant heterogeneity in node connections, resulting in a few vertices playing critical roles in various scenarios, including decision-making, viral marketing, and population immunization. Thus, identifying key vertices is a fundamental research problem in Network Science. In this paper, we introduce vertex entanglement (VE), an entanglement-based metric capable of quantifying the perturbations caused by individual vertices on spectral entropy, residing at the intersection of quantum information and network science. Our analytical analysis reveals that VE is closely related to network robustness and information transmission ability. As an application, VE offers an approach to the challenging problem of optimal network dismantling, and empirical experiments demonstrate its superiority over state-of-the-art algorithms. Furthermore, VE also contributes to the diagnosis of autism spectrum disorder (ASD), with significant distinctions in hub disruption indices based on VE between ASD and typical controls, promising a diagnostic role for VE in ASD assessment.