The topological characteristics and robustness analysis for a class of fractal weighted networks

Abstract This study investigates a fractal weighted network model to explore the topological properties and robustness of complex networks. Firstly, we systematically analyze the network’s topological characteristics by constructing hierarchical recursive and self-similar structures. These characteristics include weighted degree distribution, network density, global efficiency, and key indicators such as first-order and second-order leader-follower coherence. We also derive exact solutions for these properties. Secondly, we conduct simulation analyses using various parameter combinations, based on the computational results. This allows us to thoroughly examine the network’s first-order and second-order coherence performance under external disturbances to assess the system’s robustness. The results show that achieving an ideal convergence state is more challenging for second-order coherence than for first-order coherence, and has a more significant impact on system robustness. Lower coherence values indicate that the system exhibits stronger anti-interference capabilities under external disturbances. Furthermore, this study provides a theoretical foundation for the optimal configuration of network parameters to improve system stability, highlights the strong relationship between coherence and robustness, and establishes a basis for designing more robust and efficient complex network systems.