Numerical Linear Algebra - Markov Model - Engineering Assignment Help

Assignment Task :

Question 1 Numerical linear algebra

Questions 2 of 6—Google PageRank (25 marks) 

1. (a) Explain how the world wide web can be represented as a directed graph W. 

What is the significance of an arrow going from website i to website j?

(b) The PageRank model is based on a Markov model defined on the graph W that represents a “random surfer”. How are the transition probabilities pij of the Markov model related to the graph W? How do the transition proba- bilities have to be chosen for a node of W with no outgoing arrows? (assume for the moment that the damping factor α = 0))

(c) Which quantity calculated from a Markov model is utilised by PageRank for ranking websites? How can this quantity be interpreted in the “random surfer” model?

(d) When calculating the Markov model according to (b), not all transition probabilities pij are strictly positive.

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