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  "body": "\n## Statement\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nThen $G$ is a [[tree|0MJ0JS72DZ]] if and only if $G$ has at least one vertex and these conditions hold.\nFor any two vertices $u$ and $v$ of $G$, there is exactly one [[path|0JDE56HWQ8]] from $u$ to $v$.\n\n## Remarks\n\nExistence of a path between any two vertices is connectedness. Uniqueness of the path is equivalent to acyclicity: two different paths between the same vertices contain a cycle.\nIn a tree, the unique path from $u$ to $v$ is a shortest walk, so its length is the [[distance|0WPZ5YPAGR]] $d(u, v)$.\n\n## Explanations\n\n### L1 human\n\nIn a tree there is only one way to get from one vertex to another without going back.\nIf there were two different ways, together they would form a loop, and a tree has no loop.\n",
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