Block Dense Weighted Networks with Augmented Degree Correction
This work addresses the need for flexible and efficient modeling of dense weighted networks with community patterns, which is incremental as it builds on existing network analysis methods.
The authors tackled the problem of modeling dense weighted networks with community structure by proposing a new framework that maps node characteristics to edge weights with few parameters, and they developed a bootstrap method for generating new networks on the same vertices, showing performance through theory, simulations, and real data.
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.