  The study of networks has grown into a substantial interdisciplinary
endeavour that encompasses myriad disciplines in the natural, social, and
information sciences. Here we introduce a framework for constructing taxonomies
of networks based on their structural similarities. These networks can arise
from any of numerous sources: they can be empirical or synthetic, they can
arise from multiple realizations of a single process, empirical or synthetic,
or they can represent entirely different systems in different disciplines.
Since the mesoscopic properties of networks are hypothesized to be important
for network function, we base our comparisons on summaries of network community
structures. While we use a specific method for uncovering network communities,
much of the introduced framework is independent of that choice. After
introducing the framework, we apply it to construct a taxonomy for 746
individual networks and demonstrate that our approach usefully identifies
similar networks. We also construct taxonomies within individual categories of
networks, and in each case we expose non-trivial structure. For example we
create taxonomies for similarity networks constructed from both political
voting data and financial data. We also construct network taxonomies to compare
the social structures of 100 Facebook networks and the growth structures
produced by different types of fungi.
