  Dense networks with weighted connections often exhibit a community like
structure, where although most nodes are connected to each other, different
patterns of edge weights may emerge depending on each node's community
membership. We propose a new framework for generating and estimating dense
weighted networks with potentially different connectivity patterns across
different communities. The proposed model relies on a particular class of
functions which map individual node characteristics to the edges connecting
those nodes, allowing for flexibility while requiring a small number of
parameters relative to the number of edges. By leveraging the estimation
techniques, we also develop a bootstrap methodology for generating new networks
on the same set of vertices, which may be useful in circumstances where
multiple data sets cannot be collected. Performance of these methods are
analyzed in theory, simulations, and real data.
