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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA spanning tree of $G$ is a [[subgraph|0P11X5HKAX]] $T$ of $G$ that contains every vertex of $G$ and is a [[tree|0MJ0JS72DZ]].\n\n## Remarks\n\nA graph has a spanning tree if and only if it is connected. The node [[every connected graph has a spanning tree|04XPQT2XTC]] gives one direction.\nA spanning tree of a finite connected graph with $n$ vertices has $n - 1$ edges.\nThe complete graph $K_n$ has $n^{n-2}$ spanning trees, by [[Cayley's formula|0M2SSGSYPE]]. A [[minimum spanning tree|0Z367CGNRM]] has the least total weight.\n\n## Explanations\n\n### L1 human\n\nA spanning tree keeps all the vertices of a graph and just enough edges to stay connected without any loop.\nFor a road network, it is a smallest set of roads that still links all towns.\n",
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