Block Dense Weighted Networks with Augmented Degree Correction

TL;DR

This paper introduces a flexible framework for modeling dense weighted networks with community-specific patterns, using a function-based approach that requires few parameters and includes a bootstrap method for network generation.

Contribution

It presents a novel function-based model for dense weighted networks with community structures and develops estimation and bootstrap techniques for analysis and simulation.

Findings

The proposed model accurately captures community-specific edge weight patterns.

The bootstrap method effectively generates new networks with similar properties.

The methods perform well in theory, simulations, and real data applications.

Abstract

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.