weighted sampled graphs converge to the graphon in probability

[[concept]]

Theorem

Let $\{G_n\}$ be a sequence of weighted graphs sampled from graphon $W$. With probability at least $1-\exp \left(-\frac{n}{2\log n}\right)$, ${\delta }_{\square }(G_n,W)\le \frac{20}{\sqrt{\log n}}$ Where ${\delta }_{\square }$ is the cut metric. ie, $G_n\to W$ in probability.

Mentions

Mentions

TABLE
FROM [[]]
 
FLATTEN choice(contains(artist, this.file.link), 1, "") + choice(contains(author, this.file.link), 1, "") + choice(contains(director, this.file.link), 1, "") + choice(contains(source, this.file.link), 1, "") as direct_source
 
WHERE !direct_source

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	const file = dc.useCurrentFile();
	return <p class="dv-modified">Created {dateTime.getCreated(file)}     ֍     Last Modified {dateTime.getLastMod(file)}</p>
}