The Synergistic Effects of Structural Evolution and Attack Strategies on Network Matching Robustness

Research on network robustness has long focused on changes in the structure connectivity of networks under attacks, effectively depicting structural integrity while ignoring the exploration of functional integrity. When the core path of the network is attacked, even if it remains connected, the rapid increase in energy consumption may still trigger systematic risks. Existing studies mainly use random networks and scale-free networks as comparative models, which has become a classic research paradigm. However, real-world networks often exhibit mixed topological features. To address the above issues, this paper introduces the concept of energy from physics into bipartite networks and establishes an evaluation framework for assessing the synergistic effects of structural evolution and attack strategies on network matching robustness. We first introduce a structural parameter <i>u</i> to construct a structural evolution model, where the network's minimal matching energy distribution evolves from topological heterogeneity to random features. When <i>u</i> approaches 0, edges with the minimal matching energy concentrate on a few candidates, manifesting scale-free network features. When <i>u</i> approaches 1, the uniform distribution of the minimum-matching-energy edges corresponds to random network features. We then design three types of edge attack strategies-minimum-energy (min-E), random-energy (ran-E), and maximum-energy (max-E) attacks-simulating the impacts of critical path destruction, uniform perturbation, and redundancy removal, respectively. In addition, we construct two evaluation indicators, the average matching energy and the matching retention rate. The results show that structural evolution significantly affects network matching robustness in a nonlinear manner. Different attack strategies also exert different influence on matching robustness. Furthermore, the findings reveal the synergistic effects of the two factors on network matching robustness. The synergistic effects of redundancy capacity and network structure on matching robustness are also explored. The research deepens the understanding of network matching robustness and provides a theoretical basis for resource allocation systems to combat network attacks.