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  "body": "\n## Summary\n\nA random graph is a graph chosen at random according to a probability distribution on a set of graphs.\nThe most studied model is the [[Erdős–Rényi model|6E83YKANV3]] $G(n, p)$, in which each possible edge on $n$ labelled vertices is present independently with probability $p$.\nOne studies which properties hold with probability tending to $1$ as $n$ grows.\nThere are sharp thresholds, for example for connectivity and for the appearance of a giant component.\nRandom graphs are a main tool of the [[probabilistic method|3B55HNS754]] and a model for large real networks.\n\n## Explanations\n\n### L1 human\n\nTake $n$ dots and, for each pair of dots, flip a coin to decide whether to draw a line between them.\nThe result is a random graph.\nTypical questions are: how likely is the graph to be connected, or to contain a triangle, when $n$ is large?\nOften the answer jumps from almost never to almost always as the probability of each edge passes a critical value.\n",
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