A Random Dot Product Model for Weighted Networks

Abstract

This paper presents a generalization of the random dot product model for networks whose edge weights are drawn from a parametrized probability distribution. We focus on the case of integer weight edges and show that many previously studied models can be recovered as special cases of this generalization. Our model also determines a dimension--reducing embedding process that gives geometric interpretations of community structure and centrality. The dimension of the embedding has consequences for the derived community structure and we exhibit a stress function for determining appropriate dimensions. We use this approach to analyze a coauthorship network and voting data from the U.S. Senate.

arXiv comment35 pages, 12 Figures

References in corpus (14)

• Statistical mechanics of complex networks
• Community detection in graphs
• The architecture of complex weighted networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Analysis of weighted networks
• Stochastic blockmodels and community structure in networks
• Reaction-diffusion processes and metapopulation models in heterogeneous networks
• Centrality in Interconnected Multilayer Networks
• An efficient and principled method for detecting communities in networks
• World citation and collaboration networks: uncovering the role of geography in science
• Adapting the Stochastic Block Model to Edge-Weighted Networks
• Topological structures in the equities market network
• Null models for network data
• Recovering communities in the general stochastic block model without knowing the parameters