  We discuss the problem of extending data mining approaches to cases in which
data points arise in the form of individual graphs. Being able to find the
intrinsic low-dimensionality in ensembles of graphs can be useful in a variety
of modeling contexts, especially when coarse-graining the detailed graph
information is of interest. One of the main challenges in mining graph data is
the definition of a suitable pairwise similarity metric in the space of graphs.
We explore two practical solutions to solving this problem: one based on
finding subgraph densities, and one using spectral information. The approach is
illustrated on three test data sets (ensembles of graphs); two of these are
obtained from standard graph generating algorithms, while the graphs in the
third example are sampled as dynamic snapshots from an evolving network
simulation.
