Process edges in increasing weight, accepting an edge exactly when its endpoints lie in different current connected components of a graph. A rejected edge can never cross a later component's boundary, since components only merge. Thus each accepted edge is lightest across the cut of a graph given by one current component. The minimum spanning tree cut property proves that the final spanning tree is minimum.
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Kruskal's algorithm is a method used to find the minimum spanning tree (MST) of a connected, undirected graph. A minimum spanning tree is a subset of the edges in the graph that connects all the vertices together without any cycles and with the minimum possible total edge weight.