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Critical states are sometimes identified experimentally through power-lawstatistics or universal scaling functions. We show here that such featuresnaturally emerge from networks in self-sustained irregular regimes away fromcriticality. In these regimes, statistical physics theory of large interactingsystems predict a regime where the nodes have independent and identicallydistributed dynamics. We thus investigated the statistics of a system in whichunits are replaced by independent stochastic surrogates, and found the samepower-law statistics, indicating that these are not sufficient to establishcriticality. We rather suggest that these are universal features of large-scalenetworks when considered macroscopically. These results put caution on theinterpretation of scaling laws found in nature.

Power-law statistics and universal scaling in the absence of criticality