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  "body": "\n## Definition\n\nLet $G = (V, E)$ be a [[graph|0JD5C82QMB]] and let $S \\subseteq V$.\nThe subgraph induced by $S$ is the graph $G[S]$ with vertex set $S$ and edge set\n$$\\{ \\{u, v\\} \\in E : u, v \\in S \\}.$$\nA subgraph of this form is an induced subgraph.\n\n## Remarks\n\nAn induced subgraph is a [[subgraph|0P11X5HKAX]] that keeps every edge of $G$ between its vertices.\nIn $K_4$, every subgraph induced by $3$ vertices is a triangle. A path on these $3$ vertices is a subgraph, but it is not induced.\nA [[clique|0G52BPNPKG]] induces a complete graph, and an [[independent set|0KZJ82WEPP]] induces a graph with no edges.\n\n## Explanations\n\n### L1 human\n\nChoose some vertices and keep all the edges between them.\nThe result is the induced subgraph on those vertices.\n",
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