  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. We further incorporate these approaches with equation free
techniques, demonstrating how such data mining approaches can enhance
scientific computation of network evolution dynamics.
