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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] with vertex set $V$, and let $v \\in V$.\nThe neighbourhood of $v$ is the set\n$$N(v) = \\{ u \\in V : u \\sim v \\}$$\nof the vertices adjacent to $v$.\nThe elements of $N(v)$ are the neighbours of $v$.\n\n## Remarks\n\nThis is the open neighbourhood. It does not contain $v$, because no vertex is adjacent to itself. The closed neighbourhood is $N[v] = N(v) \\cup \\{v\\}$.\nThe [[degree|0T0F6CCS9W]] of $v$ is $|N(v)|$ when $N(v)$ is finite.\nIn the cycle with vertices $1, 2, 3, 4, 5$ in this order, $N(1) = \\{2, 5\\}$.\n\n## Explanations\n\n### L1 human\n\nThe neighbours of a vertex are the vertices joined to it by an edge.\nIn a friendship graph, the neighbourhood of a person is the set of that person's friends.\n",
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