  Community detection is the process of grouping strongly connected nodes in a
network. Many community detection methods for un-weighted networks have a
theoretical basis in a null model. Communities discovered by these methods
therefore have interpretations in terms of statistical signficance. In this
paper, we introduce a null for weighted networks called the continuous
configuration model. We use the model both as a tool for community detection
and for simulating weighted networks with null nodes. First, we propose a
community extraction algorithm for weighted networks which incorporates
iterative hypothesis testing under the null. We prove a central limit theorem
for edge-weight sums and asymptotic consistency of the algorithm under a
weighted stochastic block model. We then incorporate the algorithm in a
community detection method called CCME. To benchmark the method, we provide a
simulation framework incorporating the null to plant "background" nodes in
weighted networks with communities. We show that the empirical performance of
CCME on these simulations is competitive with existing methods, particularly
when overlapping communities and background nodes are present. To further
validate the method, we present two real-world networks with potential
background nodes and analyze them with CCME, yielding results that reveal
macro-features of the corresponding systems.
