Reply to: Influence of the reinsertion algorithm on the performance of the Vertex Entanglement method

Empirical networks possess considerable heterogeneity of node connections, leading to a small subset of vertices playing pivotal roles in network structure and function.Consequently, identifying these key vertices represents a critical challenge in network science.Recent advancements in applying quantum-based methodologies to network analysis have introduced innovative approaches for addressing this challenge.Notably, vertex entanglement (VE) 1 has been proposed, drawing inspiration from the quantum resource theory and network information theory, particularly network entanglement (NE) 2 .Network entanglement, a pioneering concept introduced by Ghavasieh et al., is innovative but encounters several conceptual and practical limitations.In our recently published paper 1 , we have extensively acknowledged previous works, particularly that of Ghavasieh et al. 2 , and have endeavoured to clearly distinguish between existing contributions and the novel aspects of our research.