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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA path in $G$ is a [[walk|0VJZM0F9YM]] $(w_0, w_1, \\dots, w_k)$ whose vertices $w_0, w_1, \\dots, w_k$ are pairwise distinct.\n\n## Remarks\n\nA path uses each edge at most once, so every path is a [[trail|062MQGP8M5]].\nA path of length $k$ has $k + 1$ vertices. Its vertices and edges form a subgraph isomorphic to the [[path graph|075WR6W3Y3]] $P_{k+1}$.\nEach walk from $u$ to $v$ contains a path from $u$ to $v$. The node [[every walk contains a path|09VZBHB33V]] states this.\n\n## Explanations\n\n### L1 human\n\nA path is a walk that never visits the same vertex twice.\nOn a map, it is a route that never passes through the same crossing again.\n",
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