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 hiding operation preserves the physical structure of the system in a certain sense. Also, two analysis tools are introduced for determining the relative importance of the edges in terms of dynamic behavior and controllability of the complex system. The analysis tools are illustrated with numerical examples.