  Data in the form of graphs, or networks, arise naturally in a number of
contexts; examples include social networks and biological networks. We are
often faced with the availability of multiple graphs on a single set of nodes.
In this article, we propose the multiple random dot product graph model for
this setting. Our proposed model leads naturally to an optimization problem,
which we solve using an efficient alternating minimization approach. We further
use this model as the basis for a new test for the hypothesis that the graphs
come from a single distribution, versus the alternative that they are drawn
from different distributions. We evaluate the performance of both the fitting
algorithm and the hypothesis test in several simulation settings, and
demonstrate empirical improvement over existing approaches. We apply these new
approaches to a Wikipedia data set and a C. elegans data set.
