a description of the network connectivity structure, see panel (f). The network used in this figure has 1000 nodes, but only 50 are shown for clarity.[]{data-label="fig1"}](main_fig_v5_low_3_reduced.pdf){width="\linewidth"}

[**Scale-free networks of coupled [ bursting]{} neurons**]{}.

We consider coupled bursting neurons with excitatory synapses [@rulkov2001] in scale-free networks (see Methods for details on simulation of scale-free networks and formulation of the model). Our techniques work equally well for spiking dynamics.

We generate a scale-free network with $N=10^4$ nodes such that the probability of having a node of degree $k$ is proportional to $k^{-\gamma}$, where $\gamma=2.53$. For this reconstruction we only need 2000 data points for each node. Again, to every pair of time series $y_i$ and $y_j$ we assign a *Pearson distance* $s_{ij}\ge0$ and the node intensity $S_{i} = \sum_{j}s_{ij}$. The empirical distribution of the intensities $S_i$ approximates the degree distribution of the network, see Fig \[fig1\](d). In the example here, the estimated structural exponent from the distribution of $S_i$ is $\gamma_{\rm est} = 3.1$, which yields a relative error of nearly 25% with respect to the true value of $\gamma$ (see also the plots in Figure \[fig2\] a)). The functional network therefore overestimates $\gamma$, which has drastic consequences for the predicted character 