A morphism \(A \xleftarrow []{} G \xrightarrow []{} B\) of \(\text {Span(Graph)}\) may be thought of as a system with parallel interfaces, where \(A\) and \(B\) are the graphs of the interface, not necessarily thought of as input and output.
Composition, by pullback, may be thought of as parallel composition (also called communicating-parallel composition and restricted product). An action of \(G \times _{B} H\) is a pair of actions of \(G\) and of \(H\) that agree on the boundary \(B\) (synchronization).
\(\text {Span(Graph)}\) is a feedback category with the following feedback operation ("place feedback"). A span of graphs \(G : X \times Y \nrightarrow Z \times Y\) is mapped to the span of graphs \(Pfb(G) : X \nrightarrow Z\) whose apex is the subgraph of \(G\) on edges where \(\pi _Y \circ \delta _1 (g) = \pi _Y \circ \delta _0 (g)\) and whose legs are compositions of the legs of \(G\) with appropriate projections.