Graph theory on grids - is there a way for me to know if there is a node in the right, left, up or down direction from a given node?

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graph

If I have a graph looking something like this

0 - 1 - 2
........|......|
.......3.....4
...............|
...............5

Note: dots have no function, and line represent edges

and I have an adjacency matrix for that graph,how do I know only from using that matrix if there is a node,for example right from node 4?

What I have tried:

If there is a conection between nodes where their number difference is more then 1,I should know that a the node is above or below the given node.In the example I have given, 2 is connected to 4,and their number difference is 2,soo 4 has to be below 2.But node 4 and 5 are a problem I don't know how to solve.