Kruskal's Spanning Tree Algorithm

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

1. Sort the edge list $E$ by weight (shortest first)
2. Initialise a set $T=\varnothing$
3. While sorted list $E$ is not empty:
   1. Dequeue the shortest edge $(u,v)$ from $E$
   2. If $T\cup \{(u,v)\}$ is acyclic:
      1. Update $T\leftarrow T\cup \{u,v\}$
4. Return tree $T$