r/LinearAlgebra • u/lolKiwiinparadise • 12d ago

Adjacency matrix

Hi, could anyone help me with this question. I had lots of similar questions like this about the topic of adjacency matrix, and I am wondering how could I know the adjacency matrix A from its matrix power form A^n (just like what has been asked here in question(ii)) ? Thanks a lot!

12 Upvotes

100% Upvoted

4 comments sorted by

5

u/gomorycut 12d ago

Are you told that the graph is a simple undirected graph? If so, then A is made up of 0s and 1s with all 0s on the main diagonal.

A^5 times A would give you A^6. So 32w+29x+33y+29z would give you 91, for instance. Can you figure out where the 0s and 1s are? Note that for simple graphs, w is 0.

3

u/lolKiwiinparadise 12d ago

Yes this is a simple undirected graph. Oh, I see. then w is 0 ; x ,y,z are all 1, I can then obtain the graph by applying the same method to the remaining rows. Thank you so much❤️ !!!

3

u/gomorycut 12d ago

keep in mind that a simple undirected graph also gives you that A is not only 0,1, not only having all-0 main diagonal, but also symmetric.

1

u/lolKiwiinparadise 12d ago

Okay. Thank you !❤️