Enhancing the global and local robustness of networks: A network motif-based approach

•Propose local network robustness measure based on all types of four-node motifs.•Propose the MBER algorithm to enhance the global and local robustness of networks.•Proposed a simplified calculation algorithm for major network motifs to streamline motif count computation during optimization.•Adapted the fast nondominated sorting approach of NSGA-II to better meet the optimization objectives of this paper. In the real world, both natural and artificial networks, may experience degradation or failure due to faults or external perturbations, which may negatively impact people's lives. Therefore, optimizing network robustness to maintain functionality under such conditions is a crucial research area. With the deepening of network robustness research, more and more studies have found that the local robustness of networks is related to network motifs. Considering the optimization of the robustness based on the global network properties (global robustness) and local robustness of the network, this paper proposes a motif-based edge rewiring algorithm (MBER), which includes the Edge Selection Algorithm, Edge Rewiring Algorithm, Simplified Calculation Algorithm for the Number of Major Network Motifs and Adjusted Nondominated Sorting Algorithm. We optimize four synthetic networks and four real-world networks using MBER and four other optimization algorithms, respectively. The results demonstrate that the MBER algorithm is more effective in enhancing the global and local robustness of networks. Additionally, we analyse the time complexity of MBER and four other optimization algorithms, revealing that the MBER algorithm exhibits the highest time complexity due to its consideration of local robustness. This paper can provide a reference for enhancing the robustness of real-world networks more comprehensively and enriches the research on network robustness enhancement.