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Abstract:
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Network analysis has become increasingly prevalent across many scientific fields. Here, we focus on the particular issue of comparing network statistics (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 is often inappropriate. We consider normalizing network statistics relative to a simple, fully parameterized reference distribution and demonstrate via simulation how this is an improvement 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 Bernoulli models as mixture components in this reference distribution can provide adjusted network statistics that are comparable across different network sizes but still describe interesting network features, all at relatively low computational expense. Finally, we apply this methodology to a collection of ecological networks derived from L.A.FANS activity location data.
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