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  "body": "\n## Definition\n\nA [[graph|0JD5C82QMB]] $G$ is connected if its vertex set is nonempty and any two vertices of $G$ are [[reachable|0J8XE7W68F]] from each other.\n\n## Remarks\n\nThe empty graph, with no vertices, is not connected under this convention. Some authors call it connected.\nA graph is connected if and only if it has exactly one [[connected component|01VVP10MWJ]].\nThe [[cycle graphs|0QQ0F12962]], the [[path graphs|075WR6W3Y3]] and the [[trees|0MJ0JS72DZ]] are connected.\n\n## Explanations\n\n### L1 human\n\nA graph is connected when it is in one piece.\nFrom any vertex you can reach any other vertex along edges.\n",
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