The following is an adjacency matrix for a graph:
Answer the following questions by examining the matrix and its powers only, not by drawing the graph:
How many walks of length 2 are there from v2 to ν3ν
A adjacency matrix for a graph:
The ijth element in A2 represents the number of walks from of length 2.The first matrix A has dimensions and the second matrix A has dimension . Since the inner dimensions are equal, we can multiply the matrices. Moreover, the product should be a
Multiply the rows of the first matrix with the columns of the second matrix (adding the products of the corresponding elements):
How many walks of length 2 are there from v3 to v4 ?
How many walks of length 3 are there from v1 to v4 ?
How many walks of length 3 are there from v2 to v3 ?
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