Core percolation on edges of complex networks

Robustness and functionality are central issues in the study of complex networks, and core percolation offers a structural means to assess these properties by identifying the core part that withstands iterative pruning. While such network characteristics are influenced not only by nodes but also by edge interactions, most existing studies have focused on node removal, leaving the role of edges largely unexplored. Here we develop an edge-centric analytical model for core percolation that defines the edge roles of leaves, roots, and core edges based on local information. Closed-form expressions are derived for the core size and for the fractions of edge roles in both undirected and directed networks. We further refine the classification to edges with multiple roles, specifying local conditions and establishing analytical expressions for their fractions. These analytical predictions are compared with numerical simulations on both model and real networks, showing good agreement. We reveal how the composition of edge roles systematically varies with the average degree of the network. By explicitly adopting an edge-based perspective, the model addresses a missing aspect in the analysis of network robustness and provides an efficient and scalable tool for characterizing structural vulnerabilities.