Seriously, what definition of "complex" or "complexity" are you using?
Physical complexity. The arrangement of molecules in the computer or the brain. The amount of information a network contains is constant if all nodes in that network have a value regardless of whether those values have meaning to a human or other intelligence.
You keep bringing up "interaction". If it's essential for you to know where the interaction is, it's between the molecules making up a compound and between the atoms making up the molecules, and between the sub-atomic particles making up the atoms. Those interactions will of course change when data passes through them, but the number of interactions between particles, the complexity, is not increasing. In order for this to be the case, the network would have to develop new nodes.