By 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