Mathematics Standard • Year 11 • Networks • Lesson 1
Introduction to Networks · Build
Read vertices, edges, degree and adjacency from an undirected network.
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 · Read the network. For V={A,B,C,D} and E={AB,AC,BC,CD}, list C’s neighbours; find each degree and the number of edges. 3 marks
Q2 · Check the degree total. Use the network above to compare the sum of the degrees with twice the number of edges. 2 marks
Q3 · Classify the network. Is the network connected and simple? Give a route from A to D. 2 marks
Q1 · Read the network
C is adjacent to A, B and D. Degrees: A=2, B=2, C=3, D=1. There are 4 edges.
Q2 · Check the degree total
2+2+3+1=8=2×4.
Q3 · Classify the network
Yes, it is connected and simple. One route is A–C–D; there are no loops or repeated edges.