  This work makes explicit the degrees of freedom involved in modeling the
dynamics of a network, or some other first-order property of a network, such as
a measurement function. In previous work, an admissible function in a network
was constructed through the evaluation of what we called oracle components.
These oracle components are defined through some minimal properties that they
are expected to obey. This is a high-level description in the sense that it is
not clear how one could design such an object. The goal is to obtain a
low-level representation of these objects by unwrapping them into their degrees
of freedom. To achieve this, we introduce two decompositions. The first one is
the more intuitive one and allows us to define the important concept of
coupling order. The second decomposition is built on top of the first one and
is valid for the class of coupling components that have finite coupling order.
Despite this requirement, we show that this is still a very useful tool for
designing coupling components with infinite coupling orders, through a limit
approach.
