Definition
A control graph is a directed representation of the steps an agent system may execute and the conditions that select what runs next. Nodes perform work. Edges encode fixed transitions, conditional routes, model-selected branches, retries, pauses, or external decisions.
Making the graph explicit lets designers see where discretion enters the system. A routing decision can be enforced by code, delegated to a model, triggered by a tool result, or held for human approval. Those choices have different reliability and security properties even when the diagram looks the same.
A control graph does not have to be acyclic. Production agents often revisit steps to repair output, gather missing information, or retry a transient failure. Cycles need budgets, termination conditions, and state rules.
Distinguish it from nearby terms
A control graph defines permitted execution structure. An execution graph represents the work instantiated for a run. A trace records the events and route that actually occurred. A knowledge graph represents entities and relationships rather than control flow.
Check your understanding
A diagram shows an edge from "review" to "deploy" but does not say whether a model, a test result, or a person chooses it. The graph is incomplete at the exact point where authority changes.