The networks chapter shows how to describe connections with points and lines, and then ask questions about them. You learn the vocabulary first, then how to draw a real situation as a network, and finally how to find an efficient route.
The chapter sits in SPM Mathematics and is part of the Form 4 Mathematics topics.
How do the four lessons connect?
Each lesson adds one layer to the same picture.
- Identifying vertices, edges and degree gives the vocabulary.
- Representing a real network as a graph turns a situation into a drawing.
- Distinguishing directed, weighted and simple graphs names the kinds of network.
- Finding efficient routes in a small weighted network uses the weights to choose a path.
What does one small network show?
Four students in a project group list who has worked together: Aiman with Bee, Aiman with Chen, Bee with Chen, and Chen with Devi. Draw each student as a vertex and each pairing as an edge. That gives 4 vertices and 4 edges.
Chen is joined to three others, so the degree of Chen is 3. If each pairing also had a number of hours spent together, the edges would carry weights, and the graph would be weighted. Those four ideas are the four lessons in one picture.
Who should start where?
If you cannot yet say what degree means, begin at lesson one. If you can name the parts but freeze on a word problem, start at lesson two. If route questions give you answers that are not the shortest, go to lesson four.
Test yourself with the networks practice set. The skill of turning a situation into a model also appears in mathematical modelling practice.
When does extra help make sense?
Network questions reward careful reading and careful drawing. A teacher who watches you draw can catch a missing edge or a double count before it spreads.
If that sounds useful, see online one-to-one Mathematics tuition and mention networks when you enquire.