Network in Graph Theory · 5.1.4
Representing information as networks
Pupils convert real information, such as connections, routes or relationships between objects or places, into a network diagram made up of vertices representing objects and edges representing connections between them. They decide whether the network requires directed edges, weighted edges, or both, based on the information given.
The official learning standard (5.1.4)
“Represent information in the form of networks.”
What it means
Pupils convert real information, such as connections, routes or relationships between objects or places, into a network diagram made up of vertices representing objects and edges representing connections between them. They decide whether the network requires directed edges, weighted edges, or both, based on the information given.
How it is examined
Paper 2 problem-solving questions often give a description or a table of relationships, such as distances between towns or connections between people, and require pupils to draw the corresponding network diagram with correctly labelled vertices and edges as part of a larger structured question.
Worked example
Four towns, J, K, L and M, may be connected by direct roads. The table shows whether a direct road exists between each pair of towns: J–K yes, J–L yes, J–M no, K–L yes, K–M yes, L–M yes.
Represent this information as a network graph.
- Represent each town as a vertex: J, K, L, M.
- Draw an edge for every pair that has a direct road: JK, JL, KL, KM, LM.
- Do not draw an edge between J and M, since no direct road exists between them.
- The resulting network has 4 vertices and 5 edges.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Does the position of the vertices on paper matter?
No. A network's structure depends only on which vertices are connected, not on their arrangement on paper.
You may place the vertices anywhere, in any layout, as long as the edges drawn match the given information exactly.
When do I need arrows or numbers on the edges?
Add an arrow when a connection has a direction, such as a one-way route. Add a number (weight) when a connection has a measurable value, such as distance, cost or time.
If neither applies, a plain line is sufficient to represent the connection.
What if two places have no direct connection?
Simply do not draw an edge between the two corresponding vertices. Leaving them unconnected correctly shows that there is no direct relationship between those two places, even though they may still be linked indirectly through other vertices.