  Network analysis has become an increasingly prevalent research tool across a
vast range of scientific fields. Here, we focus on the particular issue of
comparing network statistics, i.e. graph-level measures of network structural
features, across multiple networks that differ in size. Although "normalized"
versions of some network statistics exist, we demonstrate via simulation why
direct comparison of raw and normalized statistics is often inappropriate. We
examine a recent suggestion to normalize network statistics relative to
Erdos-Renyi random graphs and demonstrate via simulation how this is an
improvement over direct comparison, but still sometimes problematic. We propose
a new adjustment method based on a reference distribution constructed as a
mixture model of random graphs which reflect the dependence structure exhibited
in the observed networks. We show that using simple Bernoulli models as mixture
components in this reference distribution can provide adjusted network
statistics that are relatively comparable across different network sizes but
still describe interesting features of networks, and that this can be
accomplished at relatively low computational expense. Finally, we apply this
methodology to a collection of co-location networks derived from the Los
Angeles Family and Neighborhood Survey activity location data.
