Spectral coarse-graining of complex networks

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.