  Interconnected dynamic systems are a pervasive component of our modern
infrastructures. The complexity of such systems can be staggering, which
motivates simplified representations for their manipulation and analysis. This
work introduces the complete computational structure of a system as a common
baseline for comparing different simplified representations. Linear systems are
then used as a vehicle for comparing and contrasting distinct partial structure
representations. Such representations simplify the description of a system's
complete computational structure at various levels of fidelity while retaining
a full description of the system's input-output dynamic behavior. Relationships
between these various partial structure representations are detailed, and the
landscape of new realization, minimality, and model reduction problems
introduced by these representations is briefly surveyed.
