Noncommutative signal-flow graph

In automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a tool for modeling interconnected systems and state machines by mapping the edges of a directed graph to a ring or semiring. A single edge weight might represent an array of impulse responses of a complex system (see figure to the right), or a character from an alphabet picked off the input tape of a finite automaton, while the graph might represent the flow of information or state transitions.

Source: Wikipedia — Noncommutative signal-flow graph (CC BY-SA 4.0)