  Recently, it has been claimed that some complex networks are self-similar
under a convenient renormalization procedure. We present a general method to
study renormalization flows in graphs. We find that the behavior of some
variables under renormalization, such as the maximum number of connections of a
node, obeys simple scaling laws, characterized by critical exponents. This is
true for any class of graphs, from random to scale-free networks, from lattices
to hierarchical graphs. Therefore, renormalization flows for graphs are similar
as in the renormalization of spin systems. An analysis of classic
renormalization for percolation and the Ising model on the lattice confirms
this analogy. Critical exponents and scaling functions can be used to classify
graphs in universality classes, and to uncover similarities between graphs that
are inaccessible to a standard analysis.
