the procedure cannot reconstruct the community structures.[]{data-label="fig:pe"}](construction_err.pdf "fig:"){width="\linewidth"}

Predicting critical transitions in rich-clubs {#predicting-critical-transitions-in-rich-clubs .unnumbered}
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The ability to reconstruct the network and dynamics from data can be exploited to predict critical transitions that may occur when the coupling strength. In the cat brain, for example, a transition to collective dynamics in the rich-club has drastic repercussions for the functionality of the network [@zamora-lopez2010; @lopes2017].

Our goal now is to obtain data when the network is far from a collective dynamics and predict the onset of collective motion in the rich-club. The effective network can predict the onset of such collective dynamics based on a single multivariate time series for fixed coupling strength in a regime far from the synchronized state. We analyze time-series obtained simulating the dynamics at a value of the coupling strength $\Delta \alpha = 0.3$, and apply our reconstruction procedure to obtain the network structure and a model of the isolated dynamics.

[*Estimating the transition to synchronization in the rich-club.*]{} Transitions to synchronization between the bursts is possible while the fast spikes remain out of synchronization [@rulkov2001]. To estimate the transition to burst synchronization, we obtain the slow variable as a filter over the membrane potential 