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Task
The goal of this task is to implement a well known page rank algorithm in python for a large network of dataset.
In this project we will be using “network.tsv” ” graph network dataset, which contains about 1 million nodes and 3 million edges. Each row in that file represents a directed edge in the graph.The edge’s source node id is stored in the first column of the file, and the target node id is stored in the second column.
Technology used
Python 3.7.x
Graph
Page Rank algorithm
Deliverable files
We will provide the complete code in submission.py for this project.
calculate_node_degree(), calculate and store each node’s out-degree and the graph’s maximum node id.
A node’s out-degree is its number of outgoing edges. Store the out-degree in class variable "node_degree".
max_node_id refers to the highest node id in the graph. For example, suppose a graph contains the two edges (1,4) and (2,3), in the format of (source,target), the max_node_id here is 4. Store the maximum node id to class variable max_node_id.
Implementation run_pagerank()
For a simplified PageRank algorithm, where Pd( vj ) = 1/(max_node_id + 1) is provided as node_weights in the script and you will submit the output for 10 and 25 iteration runs for a damping factor of 0.85. To verify, we are providing the sample output of 5 iterations for a simplified PageRank (simplified_pagerank_iter5_sample.txt). For personalized PageRank, the Pd( ) vector will be assigned values based on your 9-digit GTID (e.g., 987654321) and you will submit the output for 10 and 25 iteration runs for a damping factor of 0.85
Description
The PageRank algorithm was first proposed to rank web pages in search results. The basic assumption is that more “important” web pages are referenced more often by other pages and thus are ranked higher. The algorithm works by considering the number and “importance” of links pointing to a page, to estimate how important that page is. PageRank outputs a probability distribution over all web pages, representing the likelihood that a person randomly surfing the web (randomly clicking on links) would arrive at those pages.
the PageRank values are the entries in the dominant eigenvector of the modified adjacency matrix in which each column’s values adds up to 1 (i.e., “column normalized”), and this eigenvector can be calculated by the power iteration method that you will implement in this question, which iterates through the graph’s edges multiple times to update the nodes’ PageRank values (“pr_values” in pagerank.py) in each iteration. For each iteration, the PageRank computation for each node in the network graph is
for each edge (𝑣𝑖 , 𝑣𝑗) from 𝑣𝑖 to 𝑣𝑗 , where
𝑣𝑗 is node 𝑗
𝑣𝑖 is node 𝑖 that points to node 𝑗
𝑜𝑢𝑡 𝑑𝑒𝑔𝑟𝑒𝑒(𝑣𝑖 ) is the number of links going out of node 𝑣𝑖
𝑃𝑅𝑡+1(𝑣𝑗) is the pagerank value of node 𝑗 at iteration 𝑡 + 1
𝑃𝑅𝑡(𝑣𝑖) is the pagerank value of node 𝑖 at iteration t
𝑑 is the damping factor; set it to the common value of 0.85 that the surfer would continue to follow links
𝑃𝑑(𝑣𝑗) is the probability of random jump that can be personalized based on use cases
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