It is well known that scale-free networks exhibit both strengths and weaknesses in terms of robustness: scalefreenetworks are highly robust to random failures but are critically vulnerable to targeted attacks that removehigh-degree nodes. Various strategies have been proposed to address this issue. In previous work Kawasumi andHasegawa: Physica A, Vol. 649, 129958 (2024), the authors considered a selective reinforcement strategy that addsedges exclusively between minimum-degree nodes and analytically demonstrated that it significantly improves therobustness against targeted attacks in degree-uncorrelated networks. In this study, we apply this approach to scalefreenetworks with degree correlations and evaluate its effectiveness in enhancing robustness against attacks. Usingexponential random graph models, we construct networks with both positive and negative degree correlations andcompare the performance of selective reinforcement with that of random reinforcement through Monte Carlo simulations.Our results show that selective reinforcement consistently improves network robustness, regardless of thepresence or sign of degree correlation, and is particularly effective in networks with negative degree correlations.Furthermore, the advantage of selective reinforcement becomes more significant as the heterogeneity of the degreedistribution increases, i.e., when the degree exponent is smaller. These findings suggest that selective reinforcementprovides an efficient and practical strategy for enhancing the robustness of complex networks, tailored to the structuralcharacteristics commonly observed in real-world systems.
Tamura et al. (Sat,) studied this question.