1.2.5 Node-node matrix

The $n\times n$ node-node matrix  of the graph is the matrix A where A(i,j)=1 if there is one arc from node i to node j. Only 1 to 1 graphs (no more than one arc from one node to another) can be represented, but loops are allowed. This matrix is also known as the ``adjacency matrix''.

The same functions used to compute the node-arc matrix (see above) of a graph are used to compute the node-node matrix: graph_2_mat and mat_2_graph. To specify that we are working with the node-node matrix, the flag 'nodenode' must be given as the last argument of these functions.

For instance, you can find below the node-node matrix of the graph corresponding to Figure 1:

$$\left(\begin{array}{cccc} 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array}\right)$$

and the node-node matrix for the same undirected graph:

$$\left(\begin{array}{cccc} 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array}\right)$$