  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.
