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We show that fractality in complex networks arises from the geometricself-similarity of their built-in hierarchical community-like structure, whichis mathematically described by the scale-invariant equation for the masses ofthe boxes with which we cover the network when determining its box dimension.This approach - grounded in both scaling theory of phase transitions andrenormalization group theory - leads to the consistent scaling theory offractal complex networks, which reveals a collection of scaling exponents anddifferent relationships between them. The exponents can be divided into twogroups: microscopic (hitherto unknown) and macroscopic, characterizingrespectively the local structure of fractal complex networks and their globalproperties. Interestingly, exponents from both groups are related to each otherand only a few of them (three out of seven) are independent, thus bridging thegap between local self-similarity and global scale-invariance of fractalnetworks. We successfully verify our findings in real networks situated invarious fields (information - the World Wide Web, biological - the human brain,and social - scientific collaboration networks) and in several fractal networkmodels.

Scaling theory of fractal complex networks: Bridging local self-similarity and global scale-invariance