Graph Mental Model: Nodes, Edges, and Work Shape

Distinguish real data dependencies from accidental sequence. Redraw a linear workflow as a graph. Use edge labels to identify parallelizable work.

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Practice quiz (8 questions)Take final exam
Learning objectives
  • Distinguish real data dependencies from accidental sequence.
  • Redraw a linear workflow as a graph.
  • Use edge labels to identify parallelizable work.
Note

This course extends the existing Agentic Engineering track. The focus is not "more prompting"; it is shaping the work: loops, fan-out, fan-in, routing, verification, cost, and convergence.

From prompt to graph

A prompt is a sentence; a graph is the shape of work. Nodes do bounded jobs. Edges carry data. If no variable crosses from one node into another, the edge is not real and the wait is wasted.

Degenerate chains

A linear script is still a graph: a degenerate one where every node waits on the previous node. The first engineering move is to cut fake arrows and widen the graph.

const graph = {
  nodes: ['researchA', 'researchB', 'reduce', 'synthesize'],
  edges: [['researchA','reduce'], ['researchB','reduce'], ['reduce','synthesize']]
};

Recap

A loop is a controlled cycle. A graph is the work shape around that cycle. The production skill is knowing which parts need model judgment, which parts are deterministic edges, and where confidence gates belong.

Graph Mental Model: Nodes, Edges, and Work Shape — Exercises

Exercise 1 — Draw the hidden graph

Take a linear workflow you already use, such as "research sources → summarize → compare → write report". Draw every step as a node. Then remove every arrow where the downstream step does not consume upstream data.

Reference solution

A strong answer identifies independent nodes and labels edges by data, not by time. Example: "source A research" and "source B research" are independent; both feed a deterministic reduce step; the reduced evidence feeds synthesis.

Exercise 2 — Write node contracts

For three nodes in your graph, define:

  • input shape
  • output shape
  • failure mode
  • downstream consumer
Reference solution

Good contracts are narrow: { topic, sourceUrl } in; { claims: [{ text, sourceUrl, confidence }] } out. Avoid "return a useful summary" because the next node cannot validate it.

Exercise 3 — Add one safety gate

Place a verifier, schema validator, budget check, or human approval gate on the edge most likely to poison downstream work.

Reference solution

For a research graph, gate unsupported claims before synthesis. For a code graph, gate findings with reproduction or a second reviewer before reporting.