network. To illustrate this, we reconstruct the statistical properties of scale-free networks.

![ [**Example of an effective network for a scale-free network where the interaction dynamics and structure are unknown.**]{} An effective network is constructed starting from a time series and provides models for the network connectivity and unit dynamics and interactions. The actual network and its degree distribution are shown in panel (a). The time series of some representative nodes are shown in panel (b). Correlation analysis of the time series yields the functional network represented in panel (c). Here, the $(i,j)$ entry of the matrix is the Pearson distance $s_{ij}$ color coded according to the key on the right, i.e. blue entries correspond to pairs of nodes having different time-series while yellow entries correspond to pairs with similar time-series. Thus one can coarsely distinguish between high- and low-degree nodes. This analysis on its own leads to a gross overestimate of the structural parameter, see panel (d). However, using this coarse classification and mathematical results on coupled systems (\[eq1\]) satisfying assumptions (i), (ii) and (iii) makes it possible to find an approximation of the evolution rule at each node, see panel (e). Using this additional information, one can obtain 