  Complex networks can model a range of different systems, from the human brain
to social connections. Some of those networks have a large number of nodes and
links, making it impractical to analyze them directly. One strategy to simplify
these systems is by creating miniaturized versions of the networks that keep
their main properties. A convenient tool that applies that strategy is the
renormalization group (RG), a methodology used in statistical physics to change
the scales of physical systems. This method consists of two steps: a coarse
grain, where one reduces the size of the system, and a rescaling of the
interactions to compensate for the information loss. This work applies RG to
complex networks by introducing a coarse-graining method based on the Laplacian
matrix. We use a field-theoretical approach to calculate the correlation
function and coarse-grain the most correlated nodes into super-nodes, applying
our method to several artificial and real-world networks. The results are
promising, with most of the networks under analysis showing self-similar
properties across different scales.
