graph bisection

[[concept]]

Topics

const fieldName = "theme"; // Your field with links
const oldPrefix = "Thoughts/01 Themes/";
const newPrefix = "Digital Garden/Topics/";
 
const relatedLinks = dv.current()[fieldName];
 
if (Array.isArray(relatedLinks)) {
    // Map over the links, replace the path, and output only clickable links
    dv.el("span",
        relatedLinks
            .map(link => {
                if (link && link.path) {
                    let newPath = link.path.startsWith(oldPrefix)
                        ? link.path.replace(oldPrefix, newPrefix)
                        : link.path;
                    return dv.fileLink(newPath);
                }
            })
            .filter(Boolean).join(", ") 
	// Remove any undefined/null items
    );
} else {
    dv.el(dv.current().theme);
}
 
 

Min/Max Bisection

Let $G$ be an undirected graph with vertices $V=[d]$ and $d$ is even. The minimum and maximum bisections of $G$ are the numbers

\text{MinBis}(G) &:= \min_{\substack{s \subseteq V \\ \lvert S \rvert = \frac{d}{2}}} \lvert E(S, V \setminus S) \rvert \\ \text{MaxBis}(G) &:= \max_{\substack{s \subseteq V \\ \lvert S \rvert = \frac{d}{2}}} \lvert E(S, V \setminus S) \rvert \end{align}$$

NOTE

We can think of the minimum bisection as a way to formulate community detection (see SBM). We want to divide a graph into two balanced subsets with as many edges as possible in each one.

References

References

See Also

Mentions

Mentions

const modules = await cJS()
 
const COLUMNS = [  
	{ id: "Name", value: page => page.$link },  
	{ id: "Last Modified", value: page => modules.dateTime.getLastMod(page) },
];  
  
return function View() {  
	const current = dc.useCurrentFile();
// Selecting `#game` pages, for example. 
	let queryString = `@page and linksto(${current.$link})`;
	let pages = dc.useQuery(queryString);
	
	// check types
	pages = pages.filter( (p) => !modules.typeCheck.checkAll(p, current) ).sort()
	
	
	return <dc.Table columns={COLUMNS} rows={pages} paging={20}/>;  
}  

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>
}