challenging synchronization-based network reconstruction from time series: a critical evaluation using Fitzhugh-Nagumo neural networks.

The reconstruction of complex networks from time series data has become a common practice in neuroscience and dynamical systems, particularly using synchronization-based measures such as phase locking value (PLV) or correlation. However, the validity of such reconstructions-especially the assumption that synchronization implies direct coupling-remains questionable. In this work, we critically investigate the relationship between structural connectivity and functional synchronization in networks of coupled FitzHugh-Nagumo (FHN) neurons. We generate synthetic networks with known topologies (regular, small-world, and scale-free) and compute pairwise synchronization from the resulting time series. A functional network is then reconstructed based on synchronization strength, and its adjacency matrix is compared with the original structural network using the Root Mean Square Error (RMSE). Our results demonstrate that high synchronization between nodes does not necessarily indicate a direct structural link, and conversely, structurally coupled nodes may remain desynchronized. These findings challenge the reliability of synchronization-based network inference methods and call for caution in interpreting functional connectivity as structural connectivity, particularly in brain network studies.