Prim's Spanning Tree Algorithm

$\text{PRIM-MST}(G)$:

1. Select a root node $r\in V$ and all adjacent edges to a Priority Queue $Q$
2. Initialise the set $T=\varnothing$
3. While queue $Q$ is not empty:
   1. Dequeue shortest edge $(u,v)$ from $Q$
   2. If $T\cup \{(u,v)\}$ is acyclic:
      1. Update $T\leftarrow T\cup \{(u,v)\}$
      2. Add to $Q$ any new edges adjacent to $u$ or $v$
4. Return tree $T$