# Graph Theory Math

> Graph structures and network analysis

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

---

## What I do
- Analyze graph properties (connectedness, cycles, cliques)
- Find shortest paths and minimum spanning trees
- Solve network flow problems
- Apply graph coloring and matching
- Study graph algorithms (DFS, BFS, Dijkstra)
- Analyze planar graphs and Euler characteristics

## When to use me
When analyzing networks, optimizing routes, or solving relationship-based problems.

## Key Concepts
- **Eulerian Path**: Visits each edge once; exists iff 0 or 2 vertices have odd degree
- **Hamiltonian Path**: Visits each vertex once; NP-complete generally
- **Shortest Path**: Dijkstra's algorithm for weighted graphs
- **Minimum Spanning Tree**: Kruskal's or Prim's algorithm
- **Max Flow-Min Cut**: Ford-Fulkerson algorithm for network flow
- **Graph Coloring**: χ(G) minimum colors for proper coloring