A network can be represented as an adjacency matrix. An adjacency matrix is a square matrix that shows the number of edges joining each pair of vertices.

Essential Further Mathematics 4ed 2012

The adjacency matrix of a graph is an  matrix. Where ‘n’ represents the number of vertices.

The ‘1’ represents that there is an edge connecting to the two vertices, and ‘0’ represents that there is no edge. Therefore in the above matrix, Row B, Column A indicates that there is an edge that goes from B to A.

NOTE: In an adjacency matrix a loop is counted as 1 edge. The loop may contribute two degrees to the vertex, but in an adjacency matrix we only count it as one edge.

Essential Further Mathematics 4ed 2012 (Fig 23.2)

Key Points about Adjacency Matrix

• If an entire row and it corresponding column has only 0s then the vertex is said to be isolated.
• The sum of the row or column gives the degree of that particular vertex.