graph-theory-math

name	graph-theory-math
description	Graph structures and network analysis
license	MIT
compatibility	opencode
metadata	{"audience":"mathematicians","category":"mathematics"}

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