The impact of topological heterogeneity on local synchronization in complex networks

Synchronization of complex networks is a widely studied phenomenon and is commonly observed in both natural and social systems. Synchronization is determined by the interplay between the network topology and the nodal dynamics. While previous studies have primarily focused on dynamical heterogeneity, the role of topological heterogeneity remains less explored. In this paper, we investigate synchronization under homogeneous nodal dynamics, emphasizing the impact of structural heterogeneity on the emergence of local synchronization. Besides, we propose a metric to detect bridge nodes that belong to one community and exchange information with other communities. The metric is based on the recording signal data of each node in a diffusion dynamic. Employing diffusion dynamics mediated by the Laplacian operator, we introduce a kernel-based measure to quantify pairwise synchronization. We identify a regime in which node pairs exhibit exceptionally strong synchronization, surpassing the level suggested by their individual self-synchronization, which we term supra-synchronization. Our analysis reveals that this phenomenon is unlikely to occur between diffusion-symmetric nodes but instead emerges in the presence of topological asymmetries, particularly between internal and bridge nodes within modular structures. Perturbation analysis of symmetric networks and two-community systems further confirms this mechanism. These findings not only reveal fundamental constraints on synchronization in complex networks but also suggest novel applications of supra-synchronization in identifying bridge nodes and refining community detection approaches.