  We show that fractality in complex networks arises from the geometric
self-similarity of their built-in hierarchical community-like structure, which
is mathematically described by the scale-invariant equation for the masses of
the boxes with which we cover the network when determining its box dimension.
This approach - grounded in both scaling theory of phase transitions and
renormalization group theory - leads to the consistent scaling theory of
fractal complex networks, which complements the collection of scaling exponents
with several new ones and reveals various relationships between them. We
propose the introduction of two classes of exponents: microscopic and
macroscopic, characterizing the local structure of fractal complex networks and
their global properties, respectively. Interestingly, exponents from both
classes are related to each other and only a few of them (three out of seven)
are independent, thus bridging the local self-similarity and global
scale-invariance in fractal networks. We successfully verify our findings in
real networks situated in various fields (information - the World Wide Web,
biological - the human brain, and social - scientific collaboration networks)
and in several fractal network models.
