Graphs (continued)

    
Transitive closure - All possible paths between all vertices.
- Indirect paths between vertices are identified and noted.
- In an unweighted graph, it shows all connections between vertices,
  * where you can get to from each vertex
- In a directed graph, it can show the minimum cost from each vertex to all other vertices.


Spanning Tree
- A subgraph that:
  * Includes all vertices
  * Has no cycles

- A minimum spanning tree is possible with a graph with weighted edges.
  
Prim's Algorithm
- After choosing initial edge (and marking it as having been chosen),
    we look to choose edges between vertices that have and haven't yet been marked
    
Kruskal
- Ordering of edges. Select cheapest edge and use if possible.
- Vertices are arranged in what is termed a 'forest'. 
    * Connected edges are listed together in sets.
    * Eventually, the spanning tree will be held in a single set
    * We want to find edges that bridge one set to another