Graph Theory & Networks · 16 lessons

In graph theory a graph is not a chart. It is a set of points, called vertices, and a set of connections between them, called edges. A road map is a graph once you keep only which places are joined.

1. 1Vertices, Edges and Degree
2. 2Simple, Complete and Bipartite Graphs
3. 3Subgraphs, Connectedness and Trees
4. 4Directed Graphs and Strong Connectedness
5. Graphs, Degree and Trees (10)
6. 5The Adjacency Matrix
7. 6Counting Walks with Matrix Powers
8. 7The Weighted Adjacency Table
9. Adjacency Matrices (10)
10. 8Walks, Trails, Paths, Circuits and Cycles
11. 9Eulerian Trails and Circuits
12. 10Hamiltonian Paths and Cycles
13. Eulerian and Hamiltonian Routes (10)
14. 11Kruskal’s Algorithm for a Spanning Tree
15. 12Prim’s Algorithm and the Matrix Method
16. 13The Chinese Postman Problem
17. 14The Traveling Salesman Problem
18. 15The Nearest-Neighbor Upper Bound
19. 16The Deleted-Vertex Lower Bound
20. Spanning Trees and Route Problems (10)