  Edges, binding together nodes within networks, have the potential to induce
dramatic transitions when specific collective failure behaviors emerge. These
changes, initially unfolding covertly and then erupting abruptly, pose
substantial, unforeseeable threats to networked systems, and are termed
explosive vulnerability. Thus, identifying influential edges capable of
triggering such drastic transitions, while minimizing cost, is of utmost
significance. Here, we address this challenge by introducing edge collective
influence (ECI), which builds upon the optimal percolation theory applied to
line graphs. ECI embodies features of both optimal and explosive percolation,
involving minimized removal costs and explosive dismantling tactic.
Furthermore, we introduce two improved versions of ECI, namely IECI and IECIR,
tailored for objectives of hidden and fast dismantling, respectively, with
their superior performance validated in both synthetic and empirical networks.
Finally, we present a dual competitive percolation (DCP) model, whose reverse
process replicates the explosive dismantling process and the trajectory of the
cost function of ECI, elucidating the microscopic mechanisms enabling ECI's
optimization. ECI and the DCP model demonstrate the profound connection 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.
