The following is an adjacency matrix for a graph: ? = [ 0 1 1 0 1 0 2 1 1 2 0 1 0 1 1 1 ] Answer the following questions by examining the matrix and its powers only, not by drawing the graph: a) How many walks of length 2 are there from v2 to v3? b) How many walks of length 2 are there from v3 to v4? c) How many walks of length 3 are there from v1 to v4? d) How many walks of length 3 are there from v2 to v3?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 74EQ
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The following is an adjacency matrix for a graph: ? = [
0 1 1 0
1 0 2 1
1 2 0 1
0 1 1 1
]
Answer the following questions by examining the matrix and its powers only, not by
drawing the graph:
a) How many walks of length 2 are there from v2 to v3?
b) How many walks of length 2 are there from v3 to v4?
c) How many walks of length 3 are there from v1 to v4?
d) How many walks of length 3 are there from v2 to v3?

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