There are at least some types of systems for which your assertion:
C’s (i.e. the set of actors/nodes) interaction with A depends on the value of A.
is not always correct:
The most simple example would be if A is a “write-only-memory”, whose value is overwritten with the value of another node irrespective of its current value and never read.
In such a situation, A’s current value only depends on the past of the rest of C, but not on its own past.
A more realistic example are networks of pulse-coupled neurons.
Here you can have parts of the network that only react to external pulses, do not feed back into the rest of the network, and are constructed such that the effect of each pulse ceases completely before the next one.
Note that the exceptional property is rather that A’s state does not influence the future of the system (and thus also itself) rather than not being dependent on itself – though the two are technically equivalent.
However, for many types of complex systems, unidirectional couplings and in particular memoryless states are not possible.
For example, ODE systems are defined through changes to their states and thus the past state always has an influence.