Consider a set of six web pages hyperlinked by the directed graph below. A 5 (a) Find the transition matrix P for the directed graph. (b) Find the probability that the surfer will be at page 5 if they begin at page 3 after four clicks (site changes). (c) Does this directed graph have any dangling nodes? Explain what a dangling node is in your answer, and how such a node is represented in the transition matrix. (d) What initial state describes a person who begins on the dangling node. If a represents this initial state, describe d'and the product pkd for k EN. s the matrix P in the prior problem a regular matrix? If yes give the lowest power of P that is positive if not explain why not.
Consider a set of six web pages hyperlinked by the directed graph below. A 5 (a) Find the transition matrix P for the directed graph. (b) Find the probability that the surfer will be at page 5 if they begin at page 3 after four clicks (site changes). (c) Does this directed graph have any dangling nodes? Explain what a dangling node is in your answer, and how such a node is represented in the transition matrix. (d) What initial state describes a person who begins on the dangling node. If a represents this initial state, describe d'and the product pkd for k EN. s the matrix P in the prior problem a regular matrix? If yes give the lowest power of P that is positive if not explain why not.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Consider a set of six web pages hyperlinked by the directed graph below.
(a) Find the transition matrix P for the directed graph.
(b) Find the probability that the surfer will be at page 5 if they begin at page 3 after four clicks (site changes).
(c) Does this directed graph have any dangling nodes? Explain what a dangling node is in your answer, and how such a node
is represented in the transition matrix.
2
(d) What initial state describes a person who begins on the dangling node. If d represents this initial state, describe d'and
the product pkd for k € N.
3. Continue problem 1,
4
2. Is the matrix P in the prior problem a regular matrix? If yes give the lowest power of P that is positive if not explain why not.
(a) Find the matrix P.
(b) Find the matrix G, the Google Matrix
5. Find the matrix II such that lim G" = II
4. Rank the the six web pages! Which would be considered most important by the Google PageRank algorithm?
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