Revisiting the power of reinsertion for optimal targets of network attack

Abstract

Understanding and improving the robustness of networks has significant applications in various areas, such as bioinformatics, transportation, critical infrastructures, and social networks. Recently, there has been a large amount of work on network dismantling, which focuses on removing an optimal set of nodes to break the network into small components with sub-extensive sizes. However, in our experiments, we found these state-of-the-art methods, although seemingly different, utilize the same refinement technique, namely reinsertion, to improve the performance. Despite being mentioned with understatement, the technique essentially plays the key role in the final performance. Without reinsertion, the current best method would deteriorate worse than the simplest heuristic ones; while with reinsertion, even the random removal strategy achieves on par with the best results. As a consequence, we, for the first time, systematically revisit the power of reinsertion in network dismantling problems. We re-implemented and compared 10 heuristic and approximate competing methods on both synthetic networks generated by four classical network models, and 18 real-world networks which cover seven different domains with varying scales. The comprehensive ablation results show that: i) HBA (High Betweenness Adaption, no reinsertion) is the most effective network dismantling strategy, however, it can only be applicable in small scale networks; ii) HDA (High Degree Adaption, with reinsertion) achieves the best balance between effectiveness and efficiency; iii) The reinsertion techniques help improve the performance for most current methods; iv) The one, which adds back the node based on that it joins the clusters minimizing the multiply of both numbers and sizes, is the most effective reinsertion strategy for most methods. Our results can be a survey reference to help further understand the current methods and thereafter design the better ones.