  Reducing the complexity of large systems described as complex networks is key
to understand them and a crucial issue is to know which properties of the
initial system are preserved in the reduced one. Here we use random walks to
design a coarse-graining scheme for complex networks. By construction the
coarse-graining preserves the slow modes of the walk, while reducing
significantly the size and the complexity of the network. In this sense our
coarse-graining allows to approximate large networks by smaller ones, keeping
most of their relevant spectral properties.
