The term is used in more than one sense. Several authors use "graph engineering" for multi-agent topology design: which agents exist, what each one owns, how work is split between them and where a person signs off. Others use it near knowledge graphs. This entry defines the sense ConvOps uses, which is about the shape of the process the agent follows, not the shape of the agent team.
The idea starts from a common failure. Teams teach an AI agent their process by adding to an instruction file. Every incident adds a paragraph, the file grows, the agent skims more of it, and nobody can say which rule shaped a given change. Graph engineering moves the process out of prose and into structure. Each workflow is short and readable. A router takes new work and sends it down one exit. Decisions detour into sub-workflows that come back. Fix loops send failed work back to an earlier step. Shared fragments keep common steps in one place. The agent never holds the whole graph, only the step it is on.
The result is that knowledge grows while the prompt does not. A lesson from an incident becomes an edit to one step, a new fragment, or a new branch, and every future run follows it.