{'fraction_non_alphanumeric': 0.014093529788597053, 'fraction_numerical': 0.0, 'mean_word_length': 5.42798353909465, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Improving Robustness of Interdependent Networks by Reducing Key Unbalanced Dependency Links

The dependency links in interdependent networks can lead to serious cascading failures when some of the network nodes are damaged. We find that the imbalance between nodes at both ends of the dependency links is one of the important reasons for a cascade of failures, which can be reduced as a whole to improve the robustness of the networks. Therefore, we propose a method to improve the robustness of interdependent networks by reducing key unbalanced dependency links. Firstly, we propose the dependency link imbalance index (DLI), which denotes the degree difference between nodes at both ends of a dependency link. And then we sort the dependency links in descending order according to the index value. The small number of the dependency links whose index values are in the forefront are called key unbalanced dependency links. By removing the key unbalanced dependency links, the imbalance of dependency links in interdependent networks is reduced in the mass, and the robustness of the networks is improved. Compared with the present random dependency links reduction strategy (RRS), key unbalanced dependency links reduction strategy (KURS) proposed in this brief can maintain the integrity and functionality of interdependent networks and improve more robustness while reducing fewer dependency links. Numerical simulations on three interdependent networks verify the effectiveness of key unbalanced dependency links reduction strategy proposed in this brief.