A Minimum Spanning Tree (MST) is the cheapest set of edges that connect graph vertices together. For instance, servers on a network or destinations on a road map. Stated differently, an MST is the sub-set of edges with the minimum possible sum of edge weights. A MST must satisfy two properties.
- Does not contain a cycle
- A path exists between every pair of vertices
Based on the definition of a MST, the following facts logically apply:
- All connected graphs have at least one MST
- There are often multiple valid MSTs for a given graph
- An MST has $n-1$ edges.
The image below is a graphical representation of an input graph and its MST.
