Commuting operations on signal-flow graphs for visualization of interconnected systems

We explore the signal flow graph as a setup for visualizing and analyzing interconnected systems. Two operations for facilitating interpretation of signal flow graphs are defined. These are hiding of unimportant nodes and elimination of self-references and it is shown that the operations commute under some conditions and that the hiding operation preserves the physical structure of the system in a certain sense. Also, the Loop Gain Index (LGI) is introduced as a measure of the relative importance of the edges in terms of dynamic behavior of the interconnected system. The LGI is illustrated with a numerical example.