Optimal dismantling of directed networks.

Network dismantling aims to identify a set of critical nodes whose removal rapidly fragments a network's connectivity and functionality, with applications in controlling epidemics, halting rumor spread, and disrupting criminal networks. While previous studies have mainly focused on undirected networks, many real-world systems are directed, such as the World Wide Web and global trade networks. In directed networks, the giant strongly connected component captures mutual reachability and enables feedback loops that sustain system functionality. Here we introduce a centrality measure called network incoherence centrality and develop a trophic analysis-based dismantling method in which nodes are removed in descending order of their scores. Tested on synthetic networks and 14 real-world directed networks, our method consistently outperforms existing approaches. It also triggers the largest connectivity avalanches, highlighting its ability to pinpoint structurally critical nodes. These findings advance understanding of structure-function relationships in directed networks and inform the design of more resilient systems.