# Rook Chess Graph Representation

I'm doing an exercise where I have an adjacency matrix for the rook's graph. I need to figure out the right graph using its 3x3 adjacency matrix composed of the following values:

9 7 3
5 2 8
1 4 6


My main doubt is: Is the matrix representing a Multigraph where I have N edges between each node ? or Is the matrix representing a weighted digraph?

Thanks so much!

• What's the source of the problem? Normally, a rook graph is a simple graph (not a multigraph) and an adjacency matrix is an $n \times n$ 0-1 matrix, where $n$ is the number of vertices in the graph. Commented Nov 24, 2018 at 16:09
• Hi Fabio, Yes, but in this exercise, they give me the matrix above and ask me the following: draw the 3 × 3 rook’s graph associated to the following chessboard. For that reason, I'm not sure if I can draw the graph as a weighted digraph or as a multigraph. Thanks for the reply! Commented Nov 24, 2018 at 16:22
• So, the exercise's text does not explicitly say the matrix is an adjacency... Perhaps it's just a way to give names to the squares of the chessboard, and hence to the vertices of the graph. Commented Nov 24, 2018 at 16:28
• So... each square is a node and the number is just the node's name ? Well, that is an interesting approach. So, maybe are 9 nodes and the edges are the connections based on rook movements. Yes, maybe that is the right way. Thanks a lot! Commented Nov 24, 2018 at 16:39