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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] and let $u, v$ be vertices of $G$.\nIf $v$ is [[reachable|0J8XE7W68F]] from $u$, the distance $d(u, v)$ is the smallest length of a [[walk|0VJZM0F9YM]] from $u$ to $v$.\nIf $v$ is not reachable from $u$, then $d(u, v) = \\infty$.\n\n## Remarks\n\nA shortest walk is a [[path|0JDE56HWQ8]], so $d(u, v)$ is also the smallest length of a path. Such a path is a geodesic.\nOn a [[connected|0FFAYNMAJZ]] graph, $d$ is a metric: $d(u, v) = 0$ only for $u = v$, it is symmetric, and it satisfies the triangle inequality.\n\n## Explanations\n\n### L1 human\n\nThe distance between two vertices is the smallest number of edges that you must cross to go from one to the other.\nIn the cycle $C_6$, opposite vertices have distance $3$.\n",
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