Network in Graph Theory

Weighted edge

An edge that carries a value such as a distance, time or cost.

EnglishWeighted edge
Bahasa MelayuTepi berpemberat
中文加权边

How it is used

In a road network the edge from town A to town B is labelled 12, meaning the road is 12 km long. If a route runs A–B–C with weights 12 and 9, the total distance is 12 + 9 = 21 km.

Where it shows up in SPM

Appears in the Network in Graph Theory chapter (Form 5). Paper 2 is where weighted edges matter most: you add the weights along a route, compare two routes to find the shorter one, or total all the weights, for example the total length of cable in a network.

Don't confuse it with

Degree of a vertexA weight is a value carried by one edge (a distance or cost), while degree counts how many edges meet at a vertex; a high degree does not mean a large weight.
Number of edges in a routeA route with fewer edges is not always shorter; you must add the weights, since three short edges can total less than two long ones.

Open the chapter: Network in Graph Theory →

Frequently asked questions

What can a weight represent?

A weight can stand for any measured quantity along an edge: distance in km, travel time in minutes, cost in ringgit, or the length of cable. Always read the question to see what the numbers mean and keep the same unit in your final answer.

How do I find the shortest route using weighted edges?

List the possible routes between the two vertices, add the weights along each one, then choose the route with the smallest total. For example, if route 1 totals 21 km and route 2 totals 19 km, route 2 is the shorter path.

Related terms

One-hour paid trial · Same-day replyfrom RM50/hr
Book a Trial Class