Network in Graph Theory
Degree of a vertex
The number of edges that meet at a vertex.
| English | Degree of a vertex |
|---|---|
| Bahasa Melayu | Darjah bucu |
| 中文 | 顶点的度数 |
How it is used
At vertex A three roads meet, so the degree of A is 3. In a network with degrees 3, 3, 2 and 2, the sum of degrees is 3 + 3 + 2 + 2 = 10, which equals twice the number of edges, so the network has 10 ÷ 2 = 5 edges.
Where it shows up in SPM
Appears in the Network in Graph Theory chapter (Form 5). Paper 1 often asks for the degree of a named vertex or the sum of all degrees; Paper 2 uses the fact that the sum of degrees is twice the number of edges to find a missing degree or edge count.
Don't confuse it with
Open the chapter: Network in Graph Theory →
Frequently asked questions
How does a loop affect the degree of a vertex?
A loop is an edge that joins a vertex to itself. It counts as 2 towards that vertex's degree, because both of its ends touch the same vertex.
So a vertex with one loop and one ordinary edge has degree 3.
Why must the sum of all degrees be an even number?
Every edge has two ends, and each end adds 1 to a degree, so each edge contributes 2 to the total of all degrees. The sum of degrees therefore equals twice the number of edges, which is always even.