  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.

Applications;Social and Information Networks;Physics and Society