Optimal dismantling of directed networks

Abstract: As a fundamental problem in network science, network dismantling focuses on identifying a set of critical nodes whose removal sharply reduces a network's connectivity and functionality. Potential applications include stopping rumor spread, blocking sentiment propagation, and controlling epidemics and pandemics. Previous studies have mainly focused on undirected networks, whereas many real-world networks are inherently directed, such as the World Wide Web and the global trade system. Moreover, the functionality of directed networks depends on the giant strongly connected component (GSCC), where nodes are mutually reachable. Considering both the directionality and heterogeneity of these networks, we propose a novel centrality measure, network incoherence (NI) centrality, and develop a trophic analysis-based dismantling (TAD) method, in which nodes are removed in descending order according to their NI centrality scores, aiming to efficiently dismantle directed networks by reducing the GSCC. When applied to a wide range of benchmark synthetic networks with varying degree heterogeneity and 15 real-world directed networks, our TAD method consistently outperforms existing state-of-the-art methods. Significantly, TAD also induces the largest maximum avalanches during the dismantling process, highlighting its ability to capture structurally critical nodes. These findings provide new insight into the structure-function relationship of directed networks and inform the design of more resilient systems against perturbations.