LaTeX
\deg(v_i)=\sum_j A_{ij}Variables
- A: adjacency matrix
- A_ij: adjacency entry
- v_i: selected vertex
How to use this formula
Computes a vertex degree by summing its row in a simple undirected graph adjacency matrix.
Important notes
- For directed graphs, row and column sums usually represent out-degree and in-degree.
- Weights change the interpretation to weighted degree.
Quick example
If row i is [0,1,1,0], then deg(v_i)=2.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For directed graphs, row and column sums usually represent out-degree and in-degree.
- For the Degree from Adjacency Matrix, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- State whether the graph is directed, weighted, simple, connected, or finite whenever the formula depends on those properties.
Worked example
If row i is [0,1,1,0], then deg(v_i)=2.
Common mistakes
- Do not omit the index or bounds in Degree from Adjacency Matrix; changing either one changes which terms are included.
- Verify the result of Degree from Adjacency Matrix with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Degree from Adjacency Matrix 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
\deg(v_i)=\sum_j A_{ij}. - 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 Degree from Adjacency Matrix used for?
Computes a vertex degree by summing its row in a simple undirected graph adjacency matrix.
Can I copy this formula as LaTeX?
Yes. Copy \deg(v_i)=\sum_j A_{ij} 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.