Adjacency Matrix - Examples

Examples

The convention followed here is that an adjacent edge counts 1 in the matrix for an undirected graph.

Labeled graph Adjacency matrix
\begin{pmatrix} 1 & 1 & 0 & 0 & 1 & 0\\ 1 & 0 & 1 & 0 & 1 & 0\\ 0 & 1 & 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0 & 1 & 1\\ 1 & 1 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0\\ \end{pmatrix}

Coordinates are 1-6.


The Nauru graph


Coordinates are 0-23.
White fields are zeros, colored fields are ones.


Directed Cayley graph of S4


As the graph is directed,
the matrix is not symmetric.
  • The adjacency matrix of a complete graph is all 1's except for 0's on the diagonal.
  • The adjacency matrix of an empty graph is a zero matrix.

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