  The renormalization group (RG) constitutes a fundamental framework in modern
theoretical physics. It allows the study of many systems showing states with
large-scale correlations and their classification in a relatively small set of
universality classes. RG is the most powerful tool for investigating
organizational scales within dynamic systems. However, the application of RG
techniques to complex networks has presented significant challenges, primarily
due to the intricate interplay of correlations on multiple scales. Existing
approaches have relied on hypotheses involving hidden geometries and based on
embedding complex networks into hidden metric spaces. Here, we present a
practical overview of the recently introduced Laplacian Renormalization Group
for heterogeneous networks. First, we present a brief overview that justifies
the use of the Laplacian as a natural extension for well-known field theories
to analyze spatial disorder. We then draw an analogy to traditional real-space
renormalization group procedures, explaining how the LRG generalizes the
concept of "Kadanoff supernodes" as block nodes that span multiple scales.
These supernodes help mitigate the effects of cross-scale correlations due to
small-world properties. Additionally, we rigorously define the LRG procedure in
momentum space in the spirit of Wilson RG. Finally, we show different analyses
for the evolution of network properties along the LRG flow following structural
changes when the network is properly reduced.
