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  "body": "\n## Summary\n\nA graphon is a symmetric measurable function $W \\colon [0, 1]^2 \\to [0, 1]$.\nGraphons are the limit objects of sequences of dense [[graphs|00C0BR7D7H]].\nA sequence converges when the density of each fixed small graph in it converges, and then the limit is a graphon.\nThey also give the most general exchangeable model of a [[random graph|TNT3DG0HRJ]].\nGraphons turn questions of [[extremal graph theory|SC5QB5F4TE]], such as [[Sidorenko's conjecture|KN2PXSCT9J]], into questions of analysis.\n\n## Explanations\n\n### L1 human\n\nDraw the adjacency matrix of a large graph as a black and white picture in a unit square, black for an edge and white for no edge.\nWhen the graph grows, the pictures can blur into a grey picture with shades between $0$ and $1$.\nThat grey picture is a graphon: the shade at a point $(x, y)$ is the probability of an edge between \"vertices\" $x$ and $y$.\nFor example, large random graphs with edge probability $1/2$ converge to the constant graphon $W = 1/2$.\n",
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