of the network. For example, the number of connections of a hub for a scale-free network is concentrated at $k_{\rm max} \sim N^{1/(\gamma - 1)}$, so the relative inaccuracy for the estimate $ k_{\rm est}$ of the maximal degree is $ k_{\rm max}/k_{\rm est}  = N^{1/\gamma - 1/  \gamma_{\rm est}}$, which is about 500%. Such inaccuracy has important repercussions for the ability to predict the emergence of collective behaviour [@pereira2010; @pereira2017].

The statistical measure used for the construction of functional network typically depend in a nonlinear way on the degrees, thus causing a distortion in the statistics. We will discuss the case of Pearson distance. Suppose that the signals $\{(y_i(t),y_i(t+1))\}$ are purely deterministic, $y_i(t+1)=g_i(y_i(t))$, and thus perfectly fall on the graphs of the functions $g_i$, that are determined by $\beta_i$ and so by the degree $k_i$ of the node. The Pearson distance $s_{ij}$ between the signal at $i$ and $j$ is going to be a number between 0 and 1, depending on how close these graphs are. Unfortunately this distance depends nonlinearly on the degrees $k_i$ and $k_j$. Devising another distance $s'_{ij}$ without the knowledge of the interaction, in general, would still carry the nonlinear dependence on the degrees. Moreover, 