The study of complex networks has pursued an understanding of macroscopicbehavior by focusing on power-laws in microscopic observables. Here, we uncovertwo universal fundamental physical principles that are at the basis of complexnetworks generation. These principles together predict the generic emergence ofdeviations from ideal power laws, which were previously discussed away byreference to the thermodynamic limit. Our approach proposes a paradigm shift inthe physics of complex networks, toward the use of power-law deviations toinfer meso-scale structure from macroscopic observations.
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