Prim's Algorithm

A Greedy algorithm that grows an MST from a starting source vertex until it spans the entire graph:

• Start with an empty minimum spanning tree $T = \{\}$.
• Pick a vertex $v$ (at random) and add it to $T$.
• Choose a vertex $u$ not in $T$, such that the edge weight from a vertex in $T$ to $u$ is the least among all such edges.
• Add $u$ to $T$. 
• Repeat the last two steps until $(N – 1)$ edges were added.