Kruskal's Time Complexity

Kruskal's time complexity is $O(E \log E)$ where $E$ is the number of edges. Sorting the edges takes $O(E \log E)$. After sorting, you process each edge once. Union-Find operations (find and union) take nearly $O(1)$ time with path compression and union by rank.

So the bottleneck is sorting. If edges are already sorted, Kruskal runs in $O(E \alpha(V))$ where $\alpha$ is the inverse Ackermann function (effectively constant).

Space complexity is $O(V)$ for the data structures used.