graph-verifier

name	graph_verifier
description	Verify small graph-theoretic claims using a local Python helper.
user-invocable	true
disable-model-invocation	true
metadata	{"openclaw":{"emoji":"📐","requires":{"bins":["bash"]}}}

Graph Verifier

Use this skill when the user asks to sanity-check a finite graph claim, inspect a small construction, or validate a graph encoding.

How to use

1. Save JSON input to /tmp/graph_input.json with the graph data.
2. Run:

exec: /workspace/skills/graph-verifier/run_graph_verifier.sh --input /tmp/graph_input.json

3. Read the JSON result from stdout.

Supported input shapes

• graph_data: NetworkX node-link JSON
• edges: list like [[1,2],[2,3]]
• adjacency: object mapping nodes to neighbor lists
• expected: optional expected values such as {"connected": true, "bipartite": false}

When to use SageMath instead

For heavy computations beyond NetworkX's capabilities, use the SageMath skill instead:

• Chromatic polynomial, Tutte polynomial
• Automorphism group computation
• Spectral analysis (characteristic polynomial, spectral radius)
• Finite field linear algebra
• Genus, planarity dual, fractional chromatic number

Use this graph-verifier for simple/fast checks: connectivity, bipartiteness, degree sequence, basic properties.