Iterative Optimization of Structural Entropy for Enhanced Network Fragmentation Analysis

Identifying and ranking influential nodes is central to tasks such as targeted immunization, misinformation containment, and resilient design. Structural entropy (SE) offers a principled, community-aware scoring rule, yet the one-shot (static) use of SE may become suboptimal after each intervention, as the residual topology and its modular structure change. We introduce iterative structural entropy (ISE), a simple yet powerful modification that recomputes SE on the residual graph before every removal, thus turning node targeting into a sequential, feedback-driven policy. We evaluate SE and ISE on seven benchmark networks using (i) cumulative structural entropy (CSE), (ii) cumulative sum of largest connected component sizes (LCCs), and (iii) dynamic panels that track average shortest-path length and diameter within the residual LCC together with a near-threshold percolation proxy (expected outbreak size). Across datasets, ISE consistently fragments earlier and more decisively than SE; on the Netscience network, ISE reduces the cumulative LCC size by 43% (RLCCs =0.567). In parallel, ISE achieves perfect discriminability (monotonicity M=1.0) among positively scored nodes on all benchmarks, while SE and degree-based baselines display method-dependent ties. These results support ISE as a practical, adaptive alternative to static SE when sequential decisions matter, delivering sharper rankings and faster structural degradation under identical measurement protocols.