induced graphon

[[concept]]

induced graphon

Let $G_n$ be a graph with $n$ nodes. The graphon induced by $G_n$ is $W_n(u,v)={\sum }_{i=1}^n{\sum }_{j=1}^n{A}_{ij}1(u\in I_i)\cdot 1(v\in I_j)$ where $1$ is the indicator function and $I_k$ is defined as

[ \frac{k-1}{n}, \frac{k}{n} )\;\;\;1 \leq k \leq n-1 \\ \left[ \frac{n-1}{n}, 1 \right] \;\;\; k=n \end{cases}$$ ^definition

Symmetric “step function” on the unit square

Example

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

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