VertexDegree

How many edge-ends meet a vertex — direction-blind (a self-loop counts twice).

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageVertexDegree✓↗

VertexDegree(g)the degree of every vertex of $g$, as a list in VertexList order.

VertexDegree(g, v)the degree of $v$ alone.

Typed signatures

Type	Package	Applies
(value, any?) -> value	combinatorics	always

Domain: Collections

Details

• Total degree, in and out combined — a directed edge counts once at each endpoint, same as an undirected one. Sums to $2|E|$ (the handshake lemma), which the tests check against an independently-computed sum on random graphs.

Examples

3 more kept as data, checked against the oracles

Basic #

A 5-vertex path — the two ends have degree 1, the rest degree 2

live ↗

In$\mathrm{VertexDegree}(\mathrm{PathGraph}(5))$Out$\bigl\lbrack1, 2, 2, 2, 1\bigr\rbrack$

The centre of a 6-vertex star has degree 5

live ↗

In$\mathrm{VertexDegree}(\mathrm{StarGraph}(6), 1)$Out$5$

About

Examples	5
Checked against	Wolfram Language 4 agree
Crosswalk	Wolfram Language

See also: AdjacencyMatrix, Graph