Geometric branching growth predicts the evolution of resilience and self-similarity in real networks
摘要
Understanding how real-world networks evolve while maintaining resilience to failures is a central challenge in network science. Previous studies on resilience have primarily focused on the structural features and associated dynamics of static networks. However, real-world networks grow and evolve over time, and the interplay between network structure and resilience during this growth remains poorly understood. In this study, we investigate the evolution of resilience in large-scale socio-economic and technological networks—including the Internet, the world trade web, and the journal citation network—over long-term historical timescales. We find that, despite sustained growth, these networks become increasingly resilient to random node failures while preserving self-similar structural organization across multiple scales. To explain this coexistence, we extend the geometric branching growth (GBG) model, which is based on a hyperbolic geometric framework capable of generating multiscale self-similar network expansion. Remarkably, the model effectively predicts both the empirically observed enhancement of resilience and the accompanying self-similar structural evolution. Further, we show that a gradual increase in average degree is the dominant factor driving resilience improvement during self-similar evolution. These results offer insight into how complex networks can evolve toward greater resilience without disrupting their self-similar structure, which may help us better understand and design resilient large-scale technological and socio-economic systems.