LaTeX
\bar d=\frac{2|E|}{|V|}Variables
- d̄: average degree
- E: edge set
- V: vertex set
How to use this formula
Computes the mean degree of a finite undirected graph.
Important notes
- Derived directly from the handshake lemma.
- Isolated vertices are included with degree zero.
Quick example
A graph with 7 vertices and 9 edges has average degree 18/7.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Derived directly from the handshake lemma.
- For the Average Graph Degree, 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
A graph with 7 vertices and 9 edges has average degree 18/7.
Common mistakes
- When copying Average Graph Degree, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Average Graph Degree with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Average Graph Degree 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
\bar d=\frac{2|E|}{|V|}. - 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 Average Graph Degree used for?
Computes the mean degree of a finite undirected graph.
Can I copy this formula as LaTeX?
Yes. Copy \bar d=\frac{2|E|}{|V|} 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.