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    If you have the adjacency n \times n matrix A_{G}, then A_{G}^{2} gives a new n \times n matrix for which the diagonal entries give the degree of each vertex in the graph. What do the non-diagonal entries represent?

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    In general, the (i,j) entry in A_G^k will be the number of walks of length k from i to j.
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    (Original post by DFranklin)
    In general, the (i,j) entry in A_G^k 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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    (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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