Are these equivalent representations (labelled graph and adjacency matrix)?

Question

This is an example from Wikipedia's page on adjacency matrices, which from the site's format seems to be suggesting equivalence between the simple diagram below, left, and the abstractly represented matrix on the right - I can't see how this is working though, as taking it as binary it doesn't read right and taking it as a coordinate map I don't understand how edges are being represented:

Kind of mystifying adjacency matrices for me right now, can anyone explain?

Answer 1

The matrix simply represents the connection between the nodes.

The entry $a_{ij}$ is:

• $1$ if the node $j$ is connected with the node $i$;
• $0$ otherwise.

See the first column. Node $1$ is connected with $1$; also nodes $2,5$ are connected with $1$.