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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA connected component of $G$ is an equivalence class of the vertices of $G$ under [[reachability|0J8XE7W68F]].\nThe subgraph induced by a connected component is also called a connected component.\n\n## Remarks\n\nThe connected components partition the vertex set. Each component, as an induced subgraph, is [[connected|0FFAYNMAJZ]].\nA graph with $n$ vertices and $m$ edges has at least $n - m$ components.\nA graph with no edges on $n$ vertices has $n$ components.\n\n## Explanations\n\n### L1 human\n\nThe connected components are the separate pieces of a graph.\nTwo vertices are in the same piece exactly when a walk joins them.\n",
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