To represent a situation as a network, decide what each vertex stands for, decide what each edge stands for, and then list every connected pair before you draw.
This lesson follows identifying vertices, edges and degree in the SPM Mathematics networks chapter.
What is the routine?
- Name the things being connected. These are the vertices.
- Write one sentence that says what an edge means.
- List every connected pair.
- Draw the vertices, then one edge per pair.
- Count vertices and edges and compare with your list.
Step 3 before step 4 is the habit that prevents missing lines.
Worked example: walkways at a school
A school has five buildings: Library, Canteen, Hall, Labs and Office. Covered walkways join Library to Canteen, Library to Office, Canteen to Hall, Canteen to Labs, and Office to Labs.
Vertices. Let L, C, H, B and O stand for the five buildings.
Edge meaning. An edge means a covered walkway directly joins two buildings.
List of pairs. LC, LO, CH, CB and OB.
That gives 5 vertices and 5 edges. The degrees are L 2, C 3, H 1, B 2 and O 2, which add to 10, equal to 2 × 5.
A useful reading: Hall has degree 1, so it can only be reached through the Canteen.
The mistake that costs marks
The common slip is to draw the network like a map and add a vertex where two walkways cross, or to draw a line for buildings that are merely close together.
| Wrong | Right | |
|---|---|---|
| Vertices | Extra dot where lines cross | Only the five buildings |
| Edges | Hall to Labs because they are nearby | Only pairs with a walkway |
| Basis | Position on the ground | The edge meaning you wrote |
Write the edge meaning first, then test every line against it.
Check yourself
Four students have worked together in pairs: Aiman with Bee, Aiman with Chen, Bee with Chen, and Chen with Devi. Draw this as a network, state the number of vertices and edges, and say who is connected to the most people.
Answer
Vertices: the four students, A (Aiman), B (Bee), C (Chen) and D (Devi). An edge means the two students have worked together.
Edges: AB, AC, BC and CD. That is 4 vertices and 4 edges.
Degrees: A 2, B 2, C 3 and D 1. The sum is 8, equal to 2 × 4. Chen is connected to the most people, with degree 3.
What to study next
Next, learn the names for the kinds of network in distinguishing directed, weighted and simple graphs. The same listing habit supports defining variables and assumptions in modelling. Log slips in the mistake log and paper-error review.
If you want a teacher to go through your drawings, see online one-to-one Mathematics tuition.