Understanding Adjacency Matrices for Digraphs?

[Marie11]

In linear algebra, we are now learning about digraphs and I am somewhat confused as to how we can obtain and use these.

How do adjacency matrices for digraphs work?
If given that a31 is a certain number (ex. a31 = 2), how could you tell which pathways account for it? Also, if the adjacency matrix has rows ABCD and columns ABCD, how would one tell in how many transitions information travels from B to all of the others? Thanks. I really need help in understanding this.

 

[HallsofIvy]

You can't tell what pathways 'account for a31=2' only that there are two pathways from node 1 to node 3. You can find how many paths go from nod1 to node2 in 2 steps by squaring the matrix, in 3 by cubing, etc. The total number of possible paths from node_n to node_m is the "mn" element of A+ A²+ A³+ ...

 

[Marie11]

Thanks!

Thanks a lot for the very appreciated explanation.