vertex degree
顶点度
Meaning in context
In a finite simple graph, the degree d(v) of a vertex v is the number of its neighbors, equivalently the number of edges incident with v.
在有限简单图中，顶点 v 的度 d(v) 是与它相邻的顶点数，也等于关联于它的边数。
Example
The center of has degree four; each other vertex has degree one.
Usage and distinctions
The neighbor-count equality uses simplicity. In multigraph degree conventions, parallel edges have multiplicity and a loop counts twice.
Recommended reading in this subject · Preparation & skip guidance
Definition sources
- Keller and Trotter — Applied Combinatorics (2016)Section 5.1, neighborhood and degree definitions; Theorem 5.9 · Checked 2026-10-14
Translation sources
- Reinhard Diestel — 图论，第五版，官方中文目录目录，§1.2「顶点度」（中文名称证据，仅目录） · Checked 2026-10-14