# Worksheet: Adjacency Matrix

In this worksheet, we will practice using a matrix to represent adjacency in a network as an application of matrices for the graph theory.

**Q1: **

Write down the adjacency matrix of the network shown.

- A
- B
- C
- D
- E

**Q2: **

When a connection in a network does not have an arrow, it is said to be ‘undirected’. An undirected connection between nodes and is equivalent to a directed connection from to together with a directed connection from to . Determine the adjacency matrix of the network shown.

- A
- B
- C
- D
- E

**Q3: **

Shown is a network whose adjacency matrix is

List all the paths of length 2 from node 1 to node 1.

- A , , , , , , , ,
- B , , , , , , , ,
- C , , , , , , , ,
- D , , , , , , , ,
- E , , , , , , , , ,

The number of paths of length from node to node is given by , the th entry of the matrix . How many paths of length 3 are there from node 1 to node 2?

- A 18 paths
- B 22 paths
- C 26 paths
- D 23 paths
- E 16 paths