  Quantifying the differences between networks is a challenging and
ever-present problem in network science. In recent years a multitude of
diverse, ad hoc solutions to this problem have been introduced. Here we propose
that simple and well-understood ensembles of random networks (such as
Erd\H{o}s-R\'{e}nyi graphs, random geometric graphs, Watts-Strogatz graphs, the
configuration model, and preferential attachment networks) are natural
benchmarks for network comparison methods. Moreover, we show that the expected
distance between two networks independently sampled from a generative model is
a useful property that encapsulates many key features of that model. To
illustrate our results, we calculate this within-ensemble graph distance and
related quantities for classic network models (and several parameterizations
thereof) using 20 distance measures commonly used to compare graphs. The
within-ensemble graph distance provides a new framework for developers of graph
distances to better understand their creations and for practitioners to better
choose an appropriate tool for their particular task.
