  We introduce, test and discuss a method for classifying and clustering data
modeled as directed graphs. The idea is to start diffusion processes from any
subset of a data collection, generating corresponding distributions for
reaching points in the network. These distributions take the form of
high-dimensional numerical vectors and capture essential topological properties
of the original dataset. We show how these diffusion vectors can be
successfully applied for getting state-of-the-art accuracies in the problem of
extracting pathways from metabolic networks. We also provide a guideline to
illustrate how to use our method for classification problems, and discuss
important details of its implementation. In particular, we present a simple
dimensionality reduction technique that lowers the computational cost of
classifying diffusion vectors, while leaving the predictive power of the
classification process substantially unaltered. Although the method has very
few parameters, the results we obtain show its flexibility and power. This
should make it helpful in many other contexts.
