Many real systems are extremely vulnerable against attacks, since they are scale-free networks as commonly existing topological structure in them. Thus, in order to improve the robustness of connectivity, several edge rewiring methods have been so far proposed by enhancing degree–degree correlations. In fact, onion-like structures with positive degree–degree correlations are optimally robust against attacks. On the other hand, recent studies suggest that the robustness and loops are strongly related to each other. Therefore, we focus on enhancing loops as a new approach for improving the robustness. In this work, we propose edge rewiring methods and evaluate the effect on the robustness by applying to real networks. Our proposed methods are two types of rewirings in preserving degrees or not for investigating the effect of the degree modification on the robustness. Numerical results show that our proposed methods improve the robustness to the level as same or more than the state-of-the-art methods. Furthermore, our work shows that the following two points are more important for further improving the robustness. First, the robustness is strongly related to loops more than degree–degree correlations. Second, it significantly improves the robustness by reducing the gap between the maximum and minimum degrees.

许多真实的系统极易受到攻击，因为它们是无标度网络，是它们中通常存在的拓扑结构。因此，为了提高连通性的鲁棒性，迄今为止已经提出了几种通过增强度-度相关性的边缘重新布线方法。实际上，具有正度-度相关性的洋葱状结构对于攻击具有最佳的鲁棒性。另一方面，最近的研究表明，鲁棒性和循环是相互密切相关的。因此，我们专注于增强循环，作为提高鲁棒性的新方法。在这项工作中，我们提出了边缘重新布线方法，并通过应用于实际网络评估了其对鲁棒性的影响。我们提出的方法是保存度或不保存度的两种类型的重新布线，用于研究度修改对鲁棒性的影响。数值结果表明，我们提出的方法将鲁棒性提高到与现有方法相同或更高的水平。此外，我们的工作表明，以下两点对于进一步提高鲁棒性更为重要。首先，鲁棒性与循环的关系远远超过度-度相关性。其次，它通过减小最大度数和最小度数之间的差距显着提高了鲁棒性。我们的工作表明，以下两点对于进一步提高鲁棒性更为重要。首先，鲁棒性与循环的关系远远超过度-度相关性。其次，它通过减小最大度数和最小度数之间的差距显着提高了鲁棒性。我们的工作表明，以下两点对于进一步提高鲁棒性更为重要。首先，鲁棒性与循环的关系远远超过度-度相关性。其次，它通过减小最大度数和最小度数之间的差距显着提高了鲁棒性。