Unveiling explosive vulnerability of networks through edge collective behavior

Edges, linking nodes in networks, can induce abrupt transitions, initially unfolding covertly and then erupting abruptly, pose substantial, unforeseeable threats when collective failures emerge. This is termed explosive vulnerability. Thus, identifying influential edges capable of triggering such drastic transitions while minimizing cost is of utmost importance. Here, we address this challenge by introducing edge collective influence (ECI), merging optimal and explosive percolation, with minimized removal costs. Furthermore, we introduce two improved versions of ECI tailored for the objectives of covert and fast dismantling, respectively. Finally, we present a dual competitive percolation (DCP) model, the reverse process of which can reproduce the explosive dismantling process and exactly match the cost function trajectory of ECI, elucidating the microscopic mechanisms enabling ECI’s optimization. ECI and the DCP model demonstrate the “duality” between optimal and explosive percolation. This work significantly deepens our comprehension of percolation and provides valuable insights into the explosive vulnerabilities arising from edge collective behaviors.