  Across all scales of the physical world, dynamical systems can often be
usefully represented as abstract networks that encode the system's units and
inter-unit interactions. Understanding how physical rules shape the topological
structure of those networks can clarify a system's function and enhance our
ability to design, guide, or control its behavior. In the emerging area of
quantum network science, a key challenge lies in distinguishing between the
topological properties that reflect a system's underlying physics and those
that reflect the assumptions of the employed conceptual model. To elucidate and
address this challenge, we study networks that represent non-equilibrium
quantum-electronic transport through quantum antidot devices -- an example of
an open, mesoscopic quantum system. The network representations correspond to
two different models of internal antidot states: a single-particle,
non-interacting model and an effective model for collective excitations
including Coulomb interactions. In these networks, nodes represent accessible
energy states and edges represent allowed transitions. We find that both models
reflect spin conservation rules in the network topology through bipartiteness
and the presence of only even-length cycles. The models diverge, however, in
the minimum length of cycle basis elements, in a manner that depends on whether
electrons are considered to be distinguishable. Furthermore, the two models
reflect spin-conserving relaxation effects differently, as evident in both the
degree distribution and the cycle-basis length distribution. Collectively,
these observations serve to elucidate the relationship between network
structure and physical constraints in quantum-mechanical models. More
generally, our approach underscores the utility of network science in
understanding the dynamics and control of quantum systems.
