# What makes prompts a graph: necessary and sufficient conditions for prompt graph engineering

arXiv: https://arxiv.org/abs/2607.27578 · HTML: https://mlsanity.com/paper/2607.27578/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 61 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 30 of 43)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [A Prompt Pattern Catalog to Enhance Prompt Engineering with ChatGPT](https://mlsanity.com/paper/2302.11382/) (2023)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [Demonstrate-Search-Predict: Composing retrieval and language models for knowledge-intensive NLP](https://mlsanity.com/paper/2212.14024/) (2022)
- [AI Chains: Transparent and Controllable Human-AI Interaction by Chaining Large Language Model Prompts](https://mlsanity.com/paper/2110.01691/) (2021)
- [An LLM Compiler for Parallel Function Calling](https://mlsanity.com/paper/2312.04511/) (2023)
- [The Landscape of Emerging AI Agent Architectures for Reasoning, Planning, and Tool Calling: A Survey](https://mlsanity.com/paper/2404.11584/) (2024)
- [PromptChainer: Chaining Large Language Model Prompts through Visual Programming](https://mlsanity.com/paper/2203.06566/) (2022)

## Built on by (most cited first, 1 of 1)

- [Forward-Deployed Full-Stack Engineering for Autonomous Cloud MLOps](https://mlsanity.com/paper/2608.29615/) (2026)

## Abstract (arXiv)

Prompts stopped being isolated strings some time ago. In real systems, one model call feeds another, retrieval interleaves with generation, routers branch, and aggregators merge parallel results. Practice converged on a single structure to hold this together: the graph. Frameworks such as LangGraph, DSPy, and Prompt Flow expose it openly, and research systems already optimize it automatically. The vocabulary, however, lags behind. Graph names, variously, a reasoning topology inside one sampling strategy, a multi-agent conversation, or an orchestration artifact, while prompt engineering still evokes writing one good string. What is missing is a reference definition treating prompts as nodes of an explicit, executable, improvable graph. We build that definition through conceptual analysis over sources with persistent identifiers, complemented by primary grey literature. We reconstruct the genealogy of the idea, from dataflow graphs and build systems, through prompt chaining and the thought topologies (chain, tree, graph), to graphs compiled and optimized as artifacts. We then propose a constitutive definition of prompt graph engineering, state its four conditions (explicit structure, separation between structure and prompt content, executable semantics, and the graph as a first-class engineering artifact), and operationalize them as an inclusion and exclusion test. We draw the boundary against six neighboring concepts and apply the test to six real systems (LangGraph, DSPy, Prompt Flow, AutoGen, CrewAI, and Claude Code subagents); it includes and excludes consistently. We close with a research agenda organized along four design tension axes. The contribution is an operational definition and a shared vocabulary for a practice that industry already exercises daily without naming precisely.