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Hallmarks of criticality, such as power-laws and scale invariance, have beenempirically found in cortical networks and it has been conjectured thatoperating at criticality entails functional advantages, such as optimalcomputational capabilities, memory, and large dynamical ranges. As criticalbehavior requires a high degree of fine tuning to emerge, some type ofself-tuning mechanism needs to be invoked. Here we show that, taking intoaccount the complex hierarchical-modular architecture of cortical networks, thesingular critical point is replaced by an extended critical-like region whichcorresponds --in the jargon of statistical mechanics-- to a Griffiths phase.Using computational and analytical approaches, we find Griffiths phases insynthetic hierarchical networks and also in empirical brain networks such asthe human connectome and the caenorhabditis elegans one. Stretched criticalregions, stemming from structural disorder, yield enhanced functionality in ageneric way, facilitating the task of self-organizing, adaptive, andevolutionary mechanisms selecting for criticality.

Griffiths phases and the stretching of criticality in brain networks