1. Connected Components Minimum Spanning Tree
Graph Algorithms 1
Connected Components
Minimum Spanning Tree

2. Problem: Connected Components
Instance:
Given an undirected graph G=(V,E)
Question:
Print out the sets of vertices that are connected to each other.
Note: A vertex u is connected to a vertex v iff there is a path connecting the vertices.

3. Connected Components Algorithm

4. Problem: Strongly Connected Components
Instance:
Given an directed graph G=(V,E)
Question:
Print out the sets of vertices that are connected to each other.
Note: A vertex u is connected to a vertex v iff there is a path connecting the u to v and a path from v to u.

5. Strongly Connected - Algorithm

6. Problem: Minimum Spanning Tree
Instance:
Given a graph G=(V,E)
Question:
What is the minimum edge weight subgraph G’=(V,E’) that can be constructed from G such that the graph G’ is connected?

7. Kruskel’s Algorithm for MST

8. Kruskel’s Algorithm Code

9. Prim’s Algorithm for MST

10. Prim’s Algorithm - Code

11. Prim’s Algorithm - Analysis