Network in Graph Theory
Edge
A line joining two vertices in a network.
| English | Edge |
|---|---|
| Bahasa Melayu | Tepi |
| 中文 | 边 |
How it is used
A network joining towns P, Q and R has edges P–Q, Q–R and P–R, so it has 3 edges forming a triangle. If a fourth edge P–Q is added as a second road, that pair now has two edges between the same vertices (a multiple edge).
Where it shows up in SPM
Central to the Network in Graph Theory chapter (Form 5). Paper 1 asks you to count edges or state the number of edges of a described network; Paper 2 uses edges as roads or cables when finding the shortest path or the sum of all weights.
Don't confuse it with
Open the chapter: Network in Graph Theory →
Frequently asked questions
What is the difference between an edge and an arc?
In an undirected network the connection is called an edge and has no direction. In a directed network the same connection is drawn with an arrow and called an arc or directed edge, showing one-way travel such as a one-way street.
Can two vertices have more than one edge between them?
Yes. Two or more edges joining the same pair of vertices are called multiple edges, for example two separate roads between the same towns.
Each edge is still counted separately when you total the edges or work out degrees.
Does the length I draw an edge affect the answer?
No. In graph theory only the connections matter, not how long or curved you draw them.
A short and a long edge are treated the same unless the edge is weighted, in which case the written weight, not the drawn length, gives its value.