Edge Importance Quantification via Second-Order Damage Index

The stability and integrity of a network structure are crucial for its functioning, and edges are great important as the basic building blocks of a network. Identifying critical edges is especially crucial for maintaining network structure. In this paper, we propose a Second-order Damage (SD) index for networks, leveraging small neighborhood information of edges to quantify their importance within the network. The design of the SD index takes into account the local network structure of the edges, allowing for a more accurate reflection of the edges' influence on network stability. To validate the effectiveness of the SD index, we compare it with seven widely used key edge identification indices, evaluating the performance of the algorithms using the complex network robustness metric. We conducted experimental evaluations on twelve complex real network models, and the results indicate that the SD index has significant advantages in identifying critical edges. Compared to the traditional methods, the SD index not only recognizes the results more accurately, but also exhibits higher reliability in network robustness assessments.