A Physics-Inspired Approach to Identifying Structurally Critical Edges in Complex Networks

Identifying structurally critical edges is fundamental to understanding and controlling the robustness of complex networks, yet existing edge-importance measures often rely on shortest-path assumptions, local heuristics, or application-specific flow information. In this paper, we propose RNES (Resistor-Network Edge Scoring), a physics-inspired, topology-driven approach that quantifies edge criticality through an electrical-network analogy: the network is modeled as a resistor network, repeatedly excited by random zero-mean current injections, and edge scores are obtained by aggregating the induced potential-drop fluctuations governed by Kirchhoff's laws, so that edges with consistently strong responses are identified as structural bottlenecks. We evaluate RNES via targeted edge attacks on six real-world networks spanning transportation, citation, routing, and social domains, where performance is assessed by dismantling curves of the largest connected component and a robustness index summarizing connectivity degradation under targeted edge removal. Experimental results show that RNES consistently achieves faster network fragmentation and the lowest robustness index across all datasets compared with representative shortest-path-based, local, flow-based, and cycle-redundancy-based benchmarks.