  Interconnected systems are an important class of mathematical models, as they
allow for the construction of complex, hierarchical, multiphysics, and
multiscale models by the interconnection of simpler subsystems. Lagrange--Dirac
mechanical systems provide a broad category of mathematical models that are
closed under interconnection, and in this paper, we develop a framework for the
interconnection of discrete Lagrange--Dirac mechanical systems, with a view
towards constructing geometric structure-preserving discretizations of
interconnected systems. This work builds on previous work on the
interconnection of continuous Lagrange--Dirac systems (Jacobs and Yoshimura
2014) and discrete Dirac variational integrators (Leok and Ohsawa 2011). We
test our results by simulating some of the continuous examples given in Jacobs
and Yoshimura 2014.
