# Cycle Detection

> Scan a pairwise comparison matrix for preference cycles and compute transitivity metrics.

- Skill: `yogsoth-ai/cycle-detection` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add yogsoth-ai/cycle-detection`
- Raw SKILL.md: https://api.skillmd.com/api/skills/yogsoth-ai/cycle-detection/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: yogsoth-ai (https://skillmd.com/u/yogsoth-ai)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/yogsoth-ai/cycle-detection

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# Cycle Detection

Scans a pairwise comparison matrix for preference cycles (A>B>C>A) and computes transitivity metrics. Identifies all minimal cycles and quantifies overall consistency.

## Execution

Runs as a subagent. Receives a comparison matrix, returns all detected cycles and transitivity scores.

## Why Subagent

Cycle detection requires graph traversal algorithms (Johnson's algorithm or DFS-based enumeration) applied to the preference digraph. Isolating this keeps algorithmic complexity out of the orchestrator.

## HARD-GATE

Output MUST contain a `cycles` array (empty if none found) and a numeric `transitivity_score` in [0, 1]. All reported cycles MUST be verifiable against the input matrix.

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## Available SOPs

Optional, no fixed order; the final leaf is always a sop.

| SOP | When to use |
| --- | --- |
| spawn-agent | Spawn a customized CC subagent with full MCP tool access. Used by SOPs that declare execution: subagent. |

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