provides a small contribution to the individual dynamics and only their cumulative effect can influence the dynamics. Therefore, the coefficients to be recovered are close to zero, and cannot be distinguished from zero terms. In this setup, sparse recovery can also uncover a model for the isolated dynamics, however, it misidentifies the network structure. We implemented the sparse recovery method to our benchmark method and could assign only $20\%$ of the nodes to the right cluster. These results are discussed in the Methods.

Remarkably, however, the effective network is able to recover the community structures (Fig. \[RC2\] (c)). To every pair of $y_i$ and $y_j$ we assign a *Pearson distance* $s_{ij}\ge0$ which measures the difference between the observed dynamics at nodes $i$ and $j$ so that $s_{ij} \approx 0$ if the attractors of $i$ and $j$ are similar and $s_{ij} \approx 1$ if they are reasonably distinguishable (see Methods for details). The higher the number of nodes with behaviour different from $i$, the larger the intensity $S_{i} = \sum_{j}s_{ij}$. The analysis of intensities $S_i$ allows us to distinguish nodes in the rich-club. Next, we find the local low-dimensional rules $g_i$ for each time series $y_i$ by applying Step (i). These 