# Graph Of Thought

> Models complex problem solving as a Directed Acyclic Graph (DAG) of thoughts, enabling node aggregation, transformation, refinement, and non-linear network reasoning.

- Skill: `felipecustodio/graph-of-thought` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add felipecustodio/graph-of-thought`
- Raw SKILL.md: https://api.skillmd.com/api/skills/felipecustodio/graph-of-thought/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: felipecustodio (https://skillmd.com/u/felipecustodio)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/felipecustodio/graph-of-thought

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## Overview & Purpose

Graph of Thought (GoT) extends beyond tree structures by representing thoughts as vertices in a Directed Acyclic Graph (DAG). This allows operations like combining multiple independent lines of reasoning (aggregation), refining existing thoughts, and forming feedback loops or complex dependencies between distinct ideas.

## When to Use

- **Non-linear Problems**: Complex dependency networks, multi-perspective synthesis, or system integrations.
- **Thought Aggregation**: Combining outputs from 2+ distinct sub-analyses into a unified synthesis node.
- **Iterative Refinement Graphs**: When an idea needs feedback or inputs from multiple prior stages simultaneously.

## Execution Workflow

1. **Define Graph Vertices (Nodes)**:
   - Identify discrete units of reasoning or hypotheses as nodes ($V_1, V_2, \dots, V_n$).

2. **Establish Directed Edges (Dependencies)**:
   - Connect nodes with directional edges indicating dependencies ($V_i \to V_j$).

3. **Perform Graph Transformations**:
   - **Aggregation**: Merge insights from $V_a$ and $V_b$ into $V_{combined}$.
   - **Refinement**: Pass $V_i$ through a critique node to produce $V_{improved}$.
   - **Branching**: Split $V_i$ into sub-hypotheses $V_{i1}$ and $V_{i2}$.

4. **Evaluate Topological Order**:
   - Process nodes according to topological dependencies to synthesize final conclusions.

## Expected Output Contract

```markdown
### Graph of Thought Representation
- **Nodes**:
  - `Node A`: [Premise / Initial Finding]
  - `Node B`: [Independent Finding]
  - `Node C (Aggregated)`: [Merged insight from A + B]
- **Edges**: `A -> C`, `B -> C`
- **Graph State**: [Topological Execution / Synthesis Summary]
```

## Scripts

- `scripts/graph_of_thought.py` - Deterministic evaluation, state validation, and CLI tool for graph-of-thought.