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  "body": "\n## Definition\n\nLet $G$ be a finite [[connected|0FFAYNMAJZ]] [[graph|0JD5C82QMB]] with edge set $E$, and let $w : E \\to \\mathbb{R}$ be a weight function.\nThe weight of a subgraph is the sum of the weights of its edges.\nA minimum spanning tree of $(G, w)$ is a [[spanning tree|0FQ5B8S1ZC]] of $G$ whose weight is the smallest among all spanning trees of $G$.\n\n## Remarks\n\nA minimum spanning tree exists, because a finite graph has finitely many spanning trees. It is unique when all weights are distinct.\nKruskal's algorithm and Prim's algorithm find a minimum spanning tree with greedy choices.\n\n## Explanations\n\n### L1 human\n\nSuppose that each road between towns has a cost to build.\nA minimum spanning tree is the cheapest set of roads that links all towns.\n",
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