Robustness and resilience of complex networks

Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their microscopic constituents. Such systems are exposed to both internal, localized, failures and external disturbances or perturbations. Owing to their interconnected structure, complex systems might be severely degraded, to the point of disintegration or systemic dysfunction. Examples include cascading failures, triggered by an initially localized overload in power systems, and the critical slowing downs of ecosystems which can be driven towards extinction. In recent years, this general phenomenon has been investigated by framing localized and systemic failures in terms of perturbations that can alter the function of a system. We capitalize on this mathematical framework to review theoretical and computational approaches to characterize robustness and resilience of complex networks. We discuss recent approaches to mitigate the impact of perturbations in terms of designing robustness, identifying early-warning signals and adapting responses. In terms of applications, we compare the performance of the state-of-the-art dismantling techniques, highlighting their optimal range of applicability for practical problems, and provide a repository with ready-to-use scripts, a much-needed tool set. Complex biological, social and engineering systems operate through intricate connectivity patterns. Understanding their robustness and resilience against disturbances is crucial for applications. This Review addresses systemic breakdown, cascading failures and potential interventions, highlighting the importance of research at the crossroad of statistical physics and machine learning. A variety of biological, social and engineering complex systems can be defined in terms of units that exchange information through interaction networks, exhibiting diverse structural patterns such as heterogeneity, modularity and hierarchy.Owing to their interconnected nature, complex networks can amplify minor disruptions to a system-wide level, making it essential to understand their robustness against both external perturbations and internal failures.The study of complex networks' robustness and resilience involves investigating phase transitions that usually depend on features such as degree connectivity, spatial embedding, interdependence and coupled dynamics.Network science offers a wide range of theoretical and computational methods for quantifying system robustness against perturbations, as well as grounded approaches to design robustness, identify early-warning signals and devise adaptive responses.These methods find application across a multitude of disciplines, including systems biology, systems neuroscience, engineering, and social and behavioural sciences.