Network in Graph Theory · 5.1.1
Networks as graphs
Students learn that a network, such as roads, computer connections, or social links, can be represented as a graph made up of vertices (points) and edges (connections joining them). They identify vertices and edges in a given network and explain what each one represents in the real situation.
The official learning standard (5.1.1)
“Recognise and explain a network as a graph.”
What it means
Students learn that a network, such as roads, computer connections, or social links, can be represented as a graph made up of vertices (points) and edges (connections joining them). They identify vertices and edges in a given network and explain what each one represents in the real situation.
How it is examined
In Paper 1, students identify the number of vertices, edges, or the degree of a vertex from a simple network diagram, usually as a multiple-choice item. In Paper 2, this concept forms the basis of longer structured questions on networks, requiring students to interpret a given diagram correctly first.
Worked example
Diagram shows a network connecting four towns P, Q, R and S by roads: P–Q, Q–R, R–S, S–P and P–R. State (a) the number of vertices, (b) the number of edges, (c) the degree of vertex P.
- The vertices are the towns themselves: P, Q, R, S. There are 4 vertices.
- The edges are the roads listed: P–Q, Q–R, R–S, S–P, P–R. There are 5 edges.
- The degree of P is the number of edges connected to P: P–Q, S–P and P–R, which is 3 edges.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's the difference between a vertex and an edge?
A vertex is a point in the graph, usually representing an object such as a town, person, or device. An edge is the line connecting two vertices, representing a relationship or connection between them, such as a road, a friendship, or a data link.
How do I find the degree of a vertex?
Count how many edges are directly connected to that vertex. If a vertex has edges going to three other vertices, its degree is 3.
Make sure to count each edge only once, even if the vertex has several connections shown in different directions on the diagram.
Can a network have more than one edge between the same two vertices?
At SPM level, network diagrams usually show at most one edge between any pair of vertices, keeping the graph simple. Focus on correctly listing each unique connection shown in the diagram rather than worrying about repeated edges, which are not typically tested at this level.