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  "body": "\n## Example\n\nLet $n$ be a natural number.\nThe complete graph $K_n$ is the [[graph|0JD5C82QMB]] with vertex set $\\{1, \\dots, n\\}$ in which any two distinct vertices are adjacent.\n\nMore generally, the complete graph on a set $V$ has an edge between each pair of distinct elements of $V$.\n\n## Remarks\n\nThe graph $K_n$ is $(n-1)$-[[regular|0KA4S8R39M]], and it has $\\binom{n}{2}$ edges. The node [[number of edges of a complete graph|05RN90E14Y]] states this.\n$K_3$ is a triangle. $K_4$ is planar, and [[$K_5$ is not planar|030A3FHN14]].\nA clique in a graph is a set of vertices that induces a complete graph.\n\n## Explanations\n\n### L1 human\n\nIn a complete graph every vertex is joined to every other vertex.\nIf $5$ people all shake hands with each other, the handshakes form $K_5$.\n",
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