LaTeX
|E(K_n)|=\frac{n(n-1)}{2}Variables
- K_n: complete graph on n vertices
- n: number of vertices
How to use this formula
Counts the edges in a simple complete graph on n vertices.
Important notes
- Every unordered pair of distinct vertices determines one edge.
- Loops and repeated edges are excluded.
Quick example
K_5 has 5·4/2=10 edges.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Every unordered pair of distinct vertices determines one edge.
- For the Complete Graph Edge Count, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- State whether the graph is directed, weighted, simple, connected, or finite whenever the formula depends on those properties.
Worked example
K_5 has 5·4/2=10 edges.
Common mistakes
- When copying Complete Graph Edge Count, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Complete Graph Edge Count with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Complete Graph Edge Count in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
|E(K_n)|=\frac{n(n-1)}{2}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Complete Graph Edge Count used for?
Counts the edges in a simple complete graph on n vertices.
Can I copy this formula as LaTeX?
Yes. Copy |E(K_n)|=\frac{n(n-1)}{2} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.