- Given an undirected graph, a spanning tree T is a subgraph of G, where T:
- These two properties make it a tree.
- Is connected.
- Is acyclic.
- This makes it spanning.
- Includes all of the vertices.
- Example:

- Spanning tree is the black edges and vertices.
- A Minimum Spanning Trees is a spanning tree of minimum total weight.
- Example: Directly connecting buildings by power lines.
- A Minimum Spanning Trees is a spanning tree of minimum total weight.
- Example: Directly connecting buildings by power lines.