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In this lesson, we will learn how to use a matrix to represent adjacency in a network as an application of matrices for the graph theory.

Q1:

Shown is a network whose adjacency matrix is

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

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?

Q2:

Write down the adjacency matrix of the network shown.

Q3:

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.

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