Reducing the size of large graphs while preserving the mechanisms that governing their dynamics remains a central challenge in network science. In this work, we introduce a graph reduction framework based on communicability-driven vertex similarity, in which pairs of structurally and dynamically equivalent vertices are iteratively merged. The method is designed to retain spectral quantities that act as proxies for diffusion, synchronization, and epidemic spreading, namely the algebraic connectivity, the Laplacian eigenratio, and the spectral radius of the adjacency matrix. We systematically evaluate the proposed approach across a diverse collection of real-world networks and benchmark it against seven representative state-of-the-art reduction techniques spanning different algorithmic paradigms. Our results show that the method enables substantially larger reductions in both vertices and edges while maintaining comparable or superior fidelity in the targeted spectral properties. Beyond average-case performance, we identify and analyze pathological scenarios associated with extreme bottleneck structures, clarify their structural origin, and propose practical strategies to mitigate their impact. Overall, the results demonstrate that communicability-based vertex merging provides a robust and flexible tool for aggressive graph reduction when the preservation of key dynamical signatures is required.
Grass-Boada et al. (2026) studied this question.