Mathematics Standard • Year 11 • Networks • Lesson 1
Introduction to Networks · Master
Translate between graph representations and explain what information a model can support.
Practice
Unless a question says otherwise, treat each network as a simple undirected graph: edges are unordered vertex pairs, with no loops or duplicate edges. Show your reasoning in the answer space; an edge list is enough.
Q1 · Verify from an edge list. A graph has V={P,Q,R,S}, E={PQ,PR,PS,QR,RS}. Find the degrees and verify their sum. 3 marks
Q2 · Test whether it is simple. A map model includes a self-loop at A. Can it be a simple graph? Identify the feature that breaks the definition. 2 marks
Q3 · State a model limitation. Vertices represent bus stops and edges represent direct services. The edge list has no times or frequencies. Give one valid inference and one unsupported inference. 2 marks
Q1 · Verify from an edge list
P=3, Q=2, R=3, S=2. The descending sequence is (3,3,2,2); the total 10 equals 2×5 edges.
Q2 · Test whether it is simple
No. A simple graph has no loops; the A–A edge breaks that condition.
Q3 · State a model limitation
It can show whether two stops have a direct service or whether a chain connects them. It cannot show the quickest or most frequent route without weights/frequency data.