Mathematics Standard • Year 11 • Networks • Lesson 2
Degree Sequences · Apply
Encode and interpret a real connection network using degree data and a matrix.
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 · Library shuttle links. Five branches P,Q,R,S,T have direct links PQ, PR, QR, QS and RT. Give the degrees in P,Q,R,S,T order. 3 marks
Q2 · Adjacency matrix. For the library network, write the 5×5 adjacency matrix in order P,Q,R,S,T. 2 marks
Q3 · Read the matrix. How many edges meet Q? How many edges are in the network? What matrix features check that it represents a simple undirected graph? 2 marks
Q1 · Library shuttle links
P=2, Q=3, R=3, S=1, T=1; degree sequence in order (2,3,3,1,1).
Q2 · Adjacency matrix
[0 1 1 0 0; 1 0 1 1 0; 1 1 0 0 1; 0 1 0 0 0; 0 0 1 0 0].
Q3 · Read the matrix
Q’s row sums to 3. The degree total is 10, so there are 5 edges. The matrix is symmetric with zeros on the diagonal.