Compute the PageRank vector of the following graph, considering the damping constant p tobe successively p = 0, p = 0.8, and respectively p = 1 max up to second iteration.
Question
Compute the PageRank vector of the following graph, considering the damping constant p tobe successively p = 0, p = 0.8, and respectively p = 1 max up to second iteration.
Solution
To compute the PageRank vector of the given graph, we will follow these steps:
Step 1: Initialize the PageRank vector.
- Assign an initial value of 1/N to each node in the graph, where N is the total number of nodes.
Step 2: Calculate the PageRank for each node.
- For each node, calculate its PageRank by summing the PageRank values of the nodes that have incoming edges to it, divided by the total number of outgoing edges from those nodes.
- Apply the damping factor p to the calculation. The damping factor represents the probability that a user will continue clicking on links rather than jumping to a random page.
Step 3: Repeat the calculation for a specified number of iterations or until convergence.
- Update the PageRank values for each node based on the calculated values from the previous step.
- Repeat this process until the PageRank values converge or until a specified number of iterations is reached.
Now, let's compute the PageRank vector for the given graph with different damping constants:
For p = 0:
- Since p = 0, there is no damping factor applied. The PageRank values will be solely based on the number of incoming edges.
- Calculate the PageRank values for each node based on the formula mentioned in Step 2.
- Repeat the calculation for the specified number of iterations or until convergence.
For p = 0.8:
- Apply the damping factor of 0.8 to the calculation of the PageRank values.
- Calculate the PageRank values for each node based on the formula mentioned in Step 2.
- Repeat the calculation for the specified number of iterations or until convergence.
For p = 1:
- Since p = 1, the damping factor is not applied. The PageRank values will be solely based on the number of incoming edges.
- Calculate the PageRank values for each node based on the formula mentioned in Step 2.
- Repeat the calculation for the specified number of iterations or until convergence.
Please note that the number of iterations and the convergence criteria may vary depending on the specific implementation or algorithm used for computing the PageRank vector.
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