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Graph Theory: What do the non-diagonal entries of the adjacency matrix squared show? watch

1. If you have the adjacency matrix , then gives a new matrix for which the diagonal entries give the degree of each vertex in the graph. What do the non-diagonal entries represent?

Many thanks
2. In general, the (i,j) entry in will be the number of walks of length k from i to j.
3. (Original post by DFranklin)
In general, the (i,j) entry in will be the number of walks of length k from i to j.
Thanks for that. Just to clarify though, does the length of a walk mean the number of edges it goes along?

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4. (Original post by Brian Moser)
Thanks for that. Just to clarify though, does the length of a walk mean the number of edges it goes along?

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The length of a walk is the number of edges that walk has.

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