  Researchers theorize that many real-world networks exhibit community
structure where within-community edges are more likely than between-community
edges. While numerous methods exist to cluster nodes into different
communities, less work has addressed this question: given some network, does it
exhibit statistically meaningful community structure? We answer this question
in a principled manner by framing it as a statistical hypothesis test in terms
of a general and model-agnostic community structure parameter. Leveraging this
parameter, we propose a simple and interpretable test statistic used to
formulate two separate hypothesis testing frameworks. The first is an
asymptotic test against a baseline value of the parameter while the second
tests against a baseline model using bootstrap-based thresholds. We prove
theoretical properties of these tests and demonstrate how the proposed method
yields rich insights into real-world data sets.
