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

Sandeco Macedo

Home/Archive/arXiv

arXiv · 2607.27578

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

Sandeco Macedo

View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Sandeco Macedo. 2026-07-30. What makes prompts a graph: necessary and sufficient conditions for prompt graph engineering. https://arxiv.org/abs/2607.27578

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Decoupling Readiness from Release for Tail-Aware Scheduling of Agentic LLM Workflows

Agentic LLM workflows consist of sequences of model turns interleaved with tool interactions, so their end-to-end completion time depends not only on inference speed but also on when ready turns are released. Most runtimes release each turn immediately upon readiness. Under contention, this eager release policy can accumulate released but unfinished work; once submitted, those turns can no longer be reordered by the workflow-level policy, increasing tail latency. We present a tail-risk-aware turn release scheduling method that jointly decides which ready turn to release next and how much released but unfinished work to maintain. The method uses a mean--Conditional Value-at-Risk (CVaR) objective to capture the evolving tail risk of unfinished workflows, incorporates online estimates of turn work when prioritizing ready turns, and adapts the released work budget to observed queue pressure. We evaluate the method using real agent execution traces from software engineering tasks across multiple LLMs and workflow arrival rates. The method performs comparably to eager release under light load and substantially reduces the P95 of workflow flow time under contention, achieving up to a \(3.50\times\) speedup.

cs.AI↗

arXiv2026

Demystifying the Privacy-Utility Trade-off in LLM Interactions

The integration of Large Language Models into daily tasks relies on context-rich instructions, inevitably exposing sensitive user information. Current privacy-preserving methods typically employ context-agnostic static rules, causing severe utility degradation. However, the specific mechanisms governing how sanitization impacts downstream performance remain largely underexplored. To address this, we conduct a systematic analysis to deconstruct the privacy-utility trade-off, uncovering three underlying mechanisms: (1) Context-Dependent Utility, which first establishes when to sanitize by revealing that data value shifts from critical constraints to dispensable noise based on user intent; (2) Strategic Adaptation, which subsequently determines how to sanitize by dictating that the choice between removal and replacement depends on the task's reliance on factual integrity versus structural coherence; and (3) Combinatorial Interplay, which finally extends the protection scope by demonstrating that attributes form a semantic web of synergistic dependencies or antagonistic redundancies. Guided by these insights, we introduce an intent-driven local protection framework. By distilling a lightweight model Veilmind-4B to drive a dynamic extraction-sanitization-restoration pipeline, our approach reaches a low-leakage privacy point while preserving substantially higher response utility than existing privacy-oriented baselines, advancing the privacy-utility trade-off toward the Pareto frontier.

cs.AI↗

arXiv2026

Defining AI Agents: A Compendium of Criteria, Metrics, and Benchmarks

The term agent in artificial intelligence lacks a standard definition, complicating the evaluation, comparison, and reproducibility of AI agent research. We address this ambiguity through a survey organized around five dimensions of agenticness: environmental interaction, learning and adaptation, autonomy, goal-directed behavior, and temporal coherence. For each dimension, we examine how the underlying capability has been conceptualized across prior work and synthesize the metrics, benchmarks, and evaluation frameworks used to assess it. This review provides a structured account of the current landscape of agent evaluation, highlighting both established approaches and areas where evaluation remains limited or inconsistent. We additionally introduce the Agent Compendium, a public-facing digital resource that organizes and extends the evaluation methods identified through this review. Together, the survey and compendium provide a common structure for evaluating and comparing agent capabilities across AI systems, supporting more reproducible research, clearer communication, and more systematic study of artificial agents.

cs.AI↗