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## Page Rank Algorithm and Implementation

PageRank (PR) is an algorithm used by Google Search to rank websites in their search engine results. PageRank was named after Larry Page, one of the founders of Google. PageRank is a way of measuring the importance of website pages. According to Google:

PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is. The underlying assumption is that more important websites are likely to receive more links from other websites.

It is not the only algorithm used by Google to order search engine results, but it is the first algorithm that was used by the company, and it is the best-known. The above centrality measure is not implemented for multi-graphs.

Algorithm   The PageRank algorithm outputs a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. PageRank can be calculated for collections of documents of any size. It is assumed in several research papers that the distribution is evenly divided among all documents in the collection at the beginning of the computational process. The PageRank computations require several passes, called “iterations”, through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.

Following is the code for the calculation of the Page rank.

The above code is the function that has been implemented in the networkx library.

To implement the above in networkx, you will have to do the following:

Below is the output, you would obtain on the IDLE after required installations.

The above code has been run on IDLE(Python IDE of windows). You would need to download the networkx library before you run this code. The part inside the curly braces represents the output. It is almost similar to Ipython(for Ubuntu users).

References

• https://en.wikipedia.org/wiki/PageRank
• https://networkx.org/documentation/stable/_modules/networkx/algorithms/link_analysis/pagerank_alg.html#pagerank
• https://www.geeksforgeeks.org/ranking-google-search-works/
• https://www.geeksforgeeks.org/google-search-works/

Thus, this way the centrality measure of Page Rank is calculated for the given graph. This way we have covered 2 centrality measures. I would like to write further on the various centrality measures used for the network analysis. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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## Improve your Coding Skills with Practice

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## Programming Assignment 3 Instructions

5 minute read

Published: July 16, 2020

Due by March 04, 2019 11:55 pm

Please note that written homework 3 is up .

## Problem Specification

Goal: In this assignment, we will compute PageRank score for the web dataset provided by Google in a programming challenge in a programming constest in 2002. Input Format: The datasets are given in txt. The file format is:

• Rows from 1 to 4: Metadata. They give information about the dataset and are self-explained.
• Following rows: each row consists of 2 values represents the link from the web page in the 1st column to the web page in the 2nd column. For example, if the row is 0 11342 , this means there is a directed link from the page id 0 to the page id 11324.

There are two dataset that we will work with in this assignment.

• web-Google_10k.txt : This dataset contains 10,000 web pages and 78323 links. The dataset can be downloaded from here . DO NOT assume that page ids are from 0 to 10,000.
• web-Google.txt : This dataset contains 875,713 web pages and 5,105,039 links. The dataset can be downloaded from here . DO NOT assume that page ids are from 0 to 875,713.

Also, it’s helpful to test your algorithm with this toy dataset . Output Format: the output format for each quesion will be specified below. There are two questions in this assigment worth 50 points total. Question 1 (20 points): Find all dead ends. A node is a dead end if it has no out-going edges or all its outoging edges points to dead ends. For example, consider the graph A->B->C->D. All nodes A,B,C,D are dead ends by this definition. D is a dead end because it has no outgoing edge. C is a dead end because its only out-going neighbor, D, is a dead end. B is a dead end for the same reason, so is A. <ol><li>(10 points) Find all dead ends of the dataset web-Google_10k.txt . For full score, your algorithm must run in less than 15 seconds . The output must be written to a file named deadends_10k.tsv </li> <li>(10 points) Find all dead ends of the dataset web-Google_800k.txt . For full score, your algorithm must run in less than 1 minute . The output must be written to a file named deadends_800k.tsv </li> </ol> The output format for Question 1 is single column, where each column is the id of an dead end. See here for a sample output for the toy dataset. Question 2 (30 points): Implement the PageRank algorithm for both datasets. The taxation parameter for both dataset is β = 0.85 and the number of PageRank iterations is T = 10. <ol> <li>(15 points)Run your algorithm for web-Google_10k.txt dataset. For full score, your algorithm must run in less than 30 seconds . The output must be written to a file named PR_10k.tsv </li> <li>(15 points)Run your algorithm for web-Google.txt dataset. For full score, your algorithm must run in less than 2 minutes . The output must be written to a file named PR_800k.tsv </li> </ol> The output format for Question 2 is two-column:

• The first column is the PageRank score.
• The second column is the corresponding web page id.

Here is a sample output for the toy dataset above. </ol> Note 1: Submit your code and output data to the Connex

Q1: How do I deal with dead ends? Answer: I deal with deadend by recursively removing dead ends from the graph until there is no dead end. Then, I calculate the PageRank for the remaining nodes. Upon having the PageRank scores, I update the score for dead ends, by the reverse removing oder. Here I stress that the update order is reverse. Q2: Do I initiate the PageRank score? Answer: You should initiate the PageRank score for each page to be the same. Remember that we only run the actual PageRank after removing dead ends. Let’s say the number of pages after removing dead ends is Np , then each node should be initialized a PageRank score of 1.0/Np. It does not matter how do you initialze PageRanke score for dead ends because they are not involved in the actual PageRank calculation. Q3: How do I know that my calculation is correct? Answer: Run your algorithm on the sample input, make sure that the order of the pages by the PageRank scores matches with that of the sample output. There may be a slight difference in the PageRanke scores itself (because of round-off error), but the oder of the pages should be unaffected.

Also, check with the following outputs, that I take 10 pages with highest PageRank scores for each dataset:

• web-Google_10k.txt : here is a sample output . This data has 1544 dead ends total.
• web-Google.txt : here is a sample output . This data has 181057 dead ends total.

Q4: What do I do if I get the out of memory error on 800K dataset? Answer: It’s probably because you construct a transition matrix to do PageRank computation. This matrix takes about 5TB (not GB) of memory, so it’s is natural that you will run out of memory. The way to get around is using a adjacency list, say L, together with the algorithm in page 21 of my note. For node i, L[i] is the set of nodes that link to i. Also, you should use a degree array D, where D[i] is the out-degree of i. That is, D[i] is the number of links from i to other nodes. Q5: How do I find dead ends efficiently? Answer: You probably want to check this out.

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## CS 377P: Programming for Performance

Assignment 2: graph algorithms, due date: 9:00 pm, february 28th, 2019.

You can do this assignment with another student in the course . Make sure you put both names on your report.

Late submission policy: Submission can be at the most 2 days late. There will be a 10% penalty for each day after the due date (cumulative).            Clarifications to the assignment will be posted at the bottom of the page.

## Description

In this assignment, you will implement a sequential program in C++ for the page-rank problem. In later assignments, you will implement parallel algorithms for page-rank and other graph problems. Read the entire assignment before starting your coding. You may use library routines from the STL and boost libraries. Graph formats We will provide three files with the following graphs: ( i ) power-law graph rmat15 , (ii) road network road-NY (New York road network) and (iii) the Wikipedia graph discussed in lecture. Graphs will be given to you in DIMACS format , which is described at the end of this assignment.

Links: rmat15.dimacs   road- NY.dimacs   wiki.dimacs

•   I/O routines for graphs :  These routines will be important for debugging your programs so make sure they are working before starting the rest of the assignment.
• Write a C++ routine that reads a graph in DIMACS format from a file and constructs a Compressed-Sparse-Row (CSR) representation of that graph in memory. Edge labels are ints for all graphs.
• Write a C++ routine that takes a graph in CSR representation in memory and prints it out to a file in DIMACS format.
• Write a C++ routine that takes a graph in CSR representation in memory, and prints node numbers and node labels, one per line, to a file.
• Page-rank algorithm : Write a push-style page-rank algorithm that operates on a graph stored in CSR format in memory, using the following specifications.
• Convergence: terminate the page-rank iterations when no node changes its page-rank value by more than 10 -4 between successive iterations.
• After the page-rank iteration is done, scale the page-rank values of all nodes so that their sum is one.

Experiments

Node degree histograms

• Write a routine that traverses a graph in CSR format and computes a histogram of the number of outgoing edges connected to each node. Use the Wikipedia example discussed in lecture to check the correctness of your code. Then compute the histograms for the rmat15 and road-NY graphs.
• Compute page-rank values for all three graphs. Verify the correctness of your implementation using the Wiki graph before running it on the other two graphs.

1.       (90 points) Submit (in canvas) your code and all the items listed in the experiments above. Also submit a makefile so that the code can be compiled with make [PARAMETER] . Describe how to compile and run the program in a README.txt. Experimental results should be submitted in PDF format.

2.       (10 points) In lecture, I mentioned that the page-rank algorithm computes the solution to a system of linear equations in which the unknowns are the page-ranks of each node and in which there is one equation for each node that defines the page-rank of that node in terms of the page-ranks of its in-neighbors. Demonstrate this with the graph from Wikipedia used in lecture, as follows.

a.       Write down the system of linear equations for the example.

b.       Using MATLAB or any other system, compute the solution to this system of equations.

c.       Does your solution match the page-ranks shown in the diagram (you may need to scale all your computed page- ranks so their sum is one)?

Turn in the answers to each of these questions.

DIMACS format for graphs

One popular format for representing directed graphs as text files is the DIMACS format (undirected graphs are represented as a directed graph by representing each undirected edge as two directed edges). Files are assumed to be well-formed and internally consistent so it is not necessary to do any error checking.  A line in a file must be one of the following.

• Comments. Comment lines give human-readable information about the file and are ignored by programs. Comment lines can appear anywhere in the file. Each comment line begins with a lower-case character c .
• Problem line. There is one problem line per input file. The problem line must appear before any node or edge descriptor lines. The problem line has the following format.

The lower-case character p signifies that this is the problem line. The FORMAT field should contain a mnemonic for the problem such as sssp . The NODES field contains an integer value specifying n , the number of nodes in the graph. The EDGES field contains an integer value specifying m , the number of edges in the graph.

• Edge Descriptors. There is one edge descriptor line for each edge in the graph, each with the following format. Each edge ( s,d ,w ) from node s to node d with weight w appears exactly once in the input file.

The lower-case character "a" signifies that this is an edge descriptor line. The "a" stands for arc, in case you are wondering. Edges may occur in any order in the file. For graphs with unweighted edges, we will use an arbitrary edge weight like 1.

Edges for rmat graphs : Special care is needed when reading in rmat graphs. Because of the generator used for rmat graphs, the files for some rmat graphs may have multiple edges between the same pair of nodes, violating the DIMACS spec. When building the CSR representation in memory, keep only the edge with the largest weight. For example, if you find edges (s d 1) and (s d 4) for example from source s to destination d, keep only the edge with weight 4. In principle, you can keep the smallest weight edge or follow some other rule, but I want everyone to follow the same rule to make grading easier.

Hints for constructing CSR format graphs from DIMACS files

· Nodes are numbered starting from 1 in DIMACS format but C++ arrays start at 0. To keep things simple and to make grading easier, your data structures and code should ignore node position 0 in your arrays.

· To construct CSR representation of graphs, you can use the following steps:

• First construct the coordinate representation (COO) of the graph from the DIMACS file. You may find std:: vector to be helpful.
• Sort edges in COO by the source node ID. You may find std:: sort() in STL to be helpful.
• Construct the CSR representation from the information in this sorted COO representation.

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## Implementing Page Rank Algorithm Assignment Help

Updated: May 11, 2022

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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

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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## Description

(this and the next assignment will follow the same structure as the previous two: you will first implement a serial version and then parallelize it.).

In the previous two assignments, you worked with structured index spaces. In this assignment, you will use unstructured index spaces to implement a well-known, and frequently implemented, graph algorithm, PageRank .

PageRank is the basis of Google’s ranking of web pages in search results. Given a directed graph where pages are nodes and the links between pages are edges, the algorithm calculates the likelihood, or rank , that a page will be visited. The rank of a page is determined recursively by the ranks of the pages that link to it. In this definition, pages that have a lot of incoming links or links from highly ranked pages are likely to be highly ranked. This idea is quite simple and yet powerful enough to produce search results that correspond well to human expectations of which pages are important. In the next section, we will see a mathematical definition of the problem and an iterative method to solve it, which you will implement in this assignment.

## The Math behind PageRank

The PageRank algorithm assumes that a web surfer is visiting some node (web page), and will either follow one of the links on that page or move to a random page (chosen from all pages on the web). The following equation recursively defines the rank P R ( p ) for each page p :

$$\mathit{PR}(p) = \frac{1 - d}{N} + d \sum_{p' \in M(p)} \frac{\mathit{PR}(p')}{L(p')}$$

where N is the number of pages, M ( p ) denotes the set of nodes with links to page p , L ( p ) is the number of outgoing links in page p , and d is the damping factor. The first term of this equation models the possibility that surfers will jump to a random web page (with probability 1 −  d ). The second term corresponds to the likelihood a surfer visits a page by following links. Note that the contribution P R ( p ′) from a neighboring page p ′ is divided by L ( p ′) (the number of p ′ 's outgoing links), which assumes each link has an equal chance to be selected.

Because of its usefulness, many researchers have explored various ways to solve this equation. In this assignment, we will pick an iterative method that is simple to implement and matches nicely with the Regent programming model.

## Iterative Method for PageRank

As the name suggests, the iterative method repeats some calculation up to convergence. Let P R ( p ;  t ) be the rank of page p at iteration t . We abuse notation for a vector p of pages: $$\mathit{PR}(\mathbf{p}; t) = (\mathit{PR}(p_0; t), \mathit{PR}(p_1; t), \dots)\\ \textrm{ where }\mathbf{p} = (p_0, p_1, \dots)$$

At iteration 0, all ranks are uniformly initialized to $\frac{1}{N}$ where N is the number of pages. $$\mathit{PR}(p; 0) = \frac{1}{N}$$ Then, the method calculates the updated ranks P R ( p ;  t  + 1) using the previous ranks P R ( p ;  t ) from this equation: $$\mathit{PR}(p; t + 1) = \frac{1 - d}{N} + d \sum_{p' \in M(p)} \frac{\mathit{PR}(p'; t)}{L(p')}$$ This equation is the same as the original one except that it is no longer recursive. The method converges when the L2-norm of the difference between the previous and current ranks is smaller than some error bound ( ϵ ): $$\left\lVert \mathit{PR}(\mathbf{p}; t + 1) - \mathit{PR}(\mathbf{p}; t) \right\rVert \le \epsilon\\$$

Your sole task in this assignment is to implement the iterative method described in the previous paragraph. Unlike the previous assignments, this assignment gives you more freedom in how you structure your code. As long as your code generates the same result as the TA's solution code (which we all know is correct), you will get full credit.

## How to run the code

File assignment3.tar.gz has the following files:

The starter code pagerank.rg and pagerank_config.rg . The code will not compile and you are supposed to see this compile error:

Some test inputs examples/*.dat . The first two lines of the inputs are the numbers of pages and edges, and the rest of them enumerate links between pages:

• The reference outputs from TA's solution code for inputs example1.dat , ..., example6.dat ( examples/references/* ). File exampleN.result.iterK corresponds to the solution at iteration K for input exampleN.dat .

The graph visualizer gen_graph.sh . Running this script on input abc.dat will give you a graph abc.pdf in the same directory. Note that visualizing a large graph can practically take forever.

Here is the complete list of options you can pass (the same list will appear with option -h ):

Although not mandatory, supporting the maximum number of iterations will be useful to compare your results with TA's solutions.

## What to submit

back to course webpage

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## Applied Social Network Analysis in Python

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## What you'll learn

Represent and manipulate networked data using the NetworkX library

Analyze the connectivity of a network

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## Skills you'll gain

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## There are 4 modules in this course

This course will introduce the learner to network analysis through tutorials using the NetworkX library. The course begins with an understanding of what network analysis is and motivations for why we might model phenomena as networks. The second week introduces the concept of connectivity and network robustness. The third week will explore ways of measuring the importance or centrality of a node in a network. The final week will explore the evolution of networks over time and cover models of network generation and the link prediction problem.

This course should be taken after: Introduction to Data Science in Python, Applied Plotting, Charting & Data Representation in Python, and Applied Machine Learning in Python.

## Why Study Networks and Basics on NetworkX

Module One introduces you to different types of networks in the real world and why we study them. You'll learn about the basic elements of networks, as well as different types of networks. You'll also learn how to represent and manipulate networked data using the NetworkX library. The assignment will give you an opportunity to use NetworkX to analyze a networked dataset of employees in a small company.

## What's included

5 videos 3 readings 1 quiz 1 programming assignment 2 ungraded labs

## 5 videos • Total 48 minutes

• Networks: Definition and Why We Study Them • 7 minutes • Preview module
• Network Definition and Vocabulary • 9 minutes
• Node and Edge Attributes • 9 minutes
• Bipartite Graphs • 12 minutes
• TA Demonstration: Loading Graphs in NetworkX • 8 minutes

## 3 readings • Total 30 minutes

• Course Syllabus • 10 minutes
• Help us learn more about you! • 10 minutes
• Notice for Auditing Learners: Assignment Submission • 10 minutes

## 1 quiz • Total 50 minutes

• Module 1 Quiz • 50 minutes

## 1 programming assignment • Total 180 minutes

• Assignment 1 • 180 minutes

## 2 ungraded labs • Total 120 minutes

• Creating and Manipulating Graphs with NetworkX • 60 minutes
• Loading Graphs in NetworkX • 60 minutes

## Network Connectivity

In Module Two you'll learn how to analyze the connectivity of a network based on measures of distance, reachability, and redundancy of paths between nodes. In the assignment, you will practice using NetworkX to compute measures of connectivity of a network of email communication among the employees of a mid-size manufacturing company.

5 videos 1 quiz 1 programming assignment 1 ungraded lab

## 5 videos • Total 55 minutes

• Clustering Coefficient • 12 minutes • Preview module
• Distance Measures • 17 minutes
• Connected Components • 9 minutes
• Network Robustness • 10 minutes
• TA Demonstration: Simple Network Visualizations in NetworkX • 6 minutes
• Module 2 Quiz • 50 minutes
• Assignment 2 • 180 minutes

## 1 ungraded lab • Total 60 minutes

• Simple Network Visualizations in NetworkX • 60 minutes

## Influence Measures and Network Centralization

In Module Three, you'll explore ways of measuring the importance or centrality of a node in a network, using measures such as Degree, Closeness, and Betweenness centrality, Page Rank, and Hubs and Authorities. You'll learn about the assumptions each measure makes, the algorithms we can use to compute them, and the different functions available on NetworkX to measure centrality. In the assignment, you'll practice choosing the most appropriate centrality measure on a real-world setting.

6 videos 1 quiz 1 programming assignment 1 discussion prompt

## 6 videos • Total 69 minutes

• Degree and Closeness Centrality • 12 minutes • Preview module
• Betweenness Centrality • 18 minutes
• Basic Page Rank • 9 minutes
• Scaled Page Rank • 8 minutes
• Hubs and Authorities • 12 minutes
• Centrality Examples • 7 minutes
• Module 3 Quiz • 50 minutes
• Assignment 3 • 180 minutes

## 1 discussion prompt • Total 15 minutes

• PageRank and Centrality in a real-life network • 15 minutes

## Network Evolution

In Module Four, you'll explore the evolution of networks over time, including the different models that generate networks with realistic features, such as the Preferential Attachment Model and Small World Networks. You will also explore the link prediction problem, where you will learn useful features that can predict whether a pair of disconnected nodes will be connected in the future. In the assignment, you will be challenged to identify which model generated a given network. Additionally, you will have the opportunity to combine different concepts of the course by predicting the salary, position, and future connections of the employees of a company using their logs of email exchanges.

3 videos 5 readings 1 quiz 1 programming assignment 1 ungraded lab

## 3 videos • Total 50 minutes

• Preferential Attachment Model • 12 minutes • Preview module
• Small World Networks • 19 minutes
• Link Prediction • 18 minutes

## 5 readings • Total 143 minutes

• Power Laws and Rich-Get-Richer Phenomena (Optional) • 40 minutes
• The Small-World Phenomenon (Optional) • 80 minutes
• Post-Course Survey • 10 minutes
• Keep Learning with Michigan Online! • 10 minutes
• Special invitation from the MADS program director • 3 minutes
• Module 4 Quiz • 50 minutes
• Assignment 4 • 180 minutes
• Extracting Features from Graphs • 60 minutes

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This was an excellent overview of using and analyzing graphs with Python. I learned a lot, got to apply my learning from previous courses, and I earned my Specialization!

Reviewed on Nov 18, 2020

I have never imagined such detailed analysis can be done on a network, nx in python is really powerful package with so many powerful functions that can do ample of analysis at a whim.

Reviewed on Nov 23, 2017

Very good class.

The lecturer is amazing!! The quizzes help you understand the concepts. The assignments are a little basic though. Overall you learn a great deal.

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## Implementing an Algorithm for Page Ranking in Java assignment help

Web-page ranking in java, get free quote, web-page ranking in java submit your homework, attached files.

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## Request Google's Page-rank Programmatically

• Download source code - 515 KB

## Introduction

Google's PageRank (PR) is a "link analysis algorithm measuring the relative importance" (PR @wikipedia ). The importance of PR nowadays is a lot lower than one or two years ago. Nevertheless, PR is the only ranking value that is public to all audience, which means it's the only factor with some transparency. For those who don't know: a PR of 10 is the highest around (like for apple.com), and 0 the lowest - those sites who don't even have a PR of 0 are in a kind of sandbox (a special filter to punish the site) or not indexed by Google.

Please forgive me for being lazy during English lessons @ school as I'm trying my best :)

Google tries to measure the relevance of a domain/site by counting the links pointing to the site/domain. This is influenced by the number of links that link to the linking site - in fact, this kind of procedure is an iterative process, which needs a lot of computing power.

49.99  $## If Helpful Share: ## Description In late 90’s as the number of webpages on the internet were growing exponentially different search engines were trying different approaches to rank the webpages. At Stanford, two computer science PhD students, Sergey Brin and Larry Page were working on the following questions: How can we trust information? Why are some web pages more important than others? Their research led to the formation of the Google search engine. In this programming assignment, you are required to implement a simplified version of the original PageRank algorithm on which Google was built. Representing the Web as a Graph The idea that the entire internet can be represented as a graph. Each node represents a webpage and each edge represents a link between two webpages. This graph can be implemented as an Adjacency Matrix or an Adjacency List. Feel free to use any data structure. Now for the sake of simplicity, we are explaining the assignment in the form of an Adjacency Matrix. We represent the graph in the form of |V|x|V| matrix where |V| is the total number of vertices in the graph. This is mapped to the webpages in the entire internet. Thus, if there is an edge from V i to V j (the from_page points to_page), we have the value in our adjacency matrix M ij = 1 and 0 otherwise. 1 2 3 4 5 M= Core Idea of PageRank • Important web pages will point to other important webpages. • Each page will have a score and the results of the search will be based on the page score (called page rank). Rank(i) = j/out_degree(j) + k/out_degree(k) Each webpage is thus a node in the directed graph and has incoming edges and outgoing edges. Each node has a rank. According to PageRank, this rank is equally split among the node’s outgoing links and this rank is equal to the sum of the incoming ranks. The rank is based on the indegree (the number of nodes pointing to it) and the importance of incoming node. This is important considering let’s say you create your personal website and have a million links to other pages of importance. If this was not the case and rank used out links, we can easily dupe the algorithm. Therefore, the rank is based on in-links. In this assignment, you need to compute the rank of the webpages using a Simplified Algorithm explained in the example below. Line 1 contains the number of lines (n) that will follow and the number of power iterations you need to perform. Each line from 2 to n will contain two URL’s – from_page to_page separated by a space. This means from_page points to the URL to_page. Print the PageRank of all pages after n powerIterations in ascending alphabetical order of webpage. Also, round off the rank of the page to two decimal places. ## Explanation through a Core Example google.com maps.com facebook.com ufl.edu ufl.edu google.com ufl.edu gmail.com maps.com facebook.com gmail.com maps.com Output facebook.com 0.20 gmail.com 0.20 google.com 0.10 maps.com 0.30 ufl.edu 0.20 Step 1: Mapping for Simplicity (Optional but you will need a mechanism to store unique vertices) Use a map/array to map the URL’s with a unique id Data Structure 1 Step 2: Graph Representation and Page Rank In page rank, the equation for your graph is given as follows:- Rank of a Page, r= M.r where, M is the matrix with values given by the following: M ij = 1/d j if there is an edge from V j to V i (d j is the outdegree of node j) For our graph, the adjacency matrix, M will look like: • 2 3 4 5 Step 3: Power iteration, r(t+1)=M.r(t) This means that a rank of the webpage at time t+1 is equal to the rank of that page at time t multiplied by matrix, M. To achieve this, we create our matrix M based on input. Next, we initialize r(t) which is a matrix of size |V|x1 and consists of the ranks of every webpage. We initialize r(t) to 1/|V|. Next we compute power_iterations based on our input. r(0) M 1 1 2 3 4 5 1 2 3 4 5 1 1 r(t+1)=r(0+1)=r(1) =M.r(0)= 2 = 3 4 5 M x r(0) = r(1) In this input case, the number of power_iterations is 2, if it is 1 then return the initializing rank matrix or r(0). If iterations>2, the process repeats where you multiply the matrix, M with the new rank matrix r(t+1) at the next iteration. Stepik Test Case Two Explanation:- (Power_iteration=3) 1 2 3 4 5 1 1 r(t+1)=r(1+1)=r(2) =M.r(1)= 2 = M x r(1) = r(2) You are allowed to use your own template but make sure your code passes the sample test cases. An example template to think about the problem is : Class AdjacencyListorMatrix { private: //Think about what member variables you need to initialize public: //Think about what helper functions you will need in the algorithm void AdjacencyListorMatrix::PageRank(int n){ } // prints the PageRank of all pages after n powerIterations in ascending alphabetical order of webpage and rounding rank to two decimal places] // This class and method are optional. To accept input, you can use this method: int no_of_lines, power_iterations; std::string from, to; std::cin >> no_of_lines; std::cin >> power_iterations; for(int i=0;i< no_of_lines;i++) { std::cin>>from; std::cin>>to; // Do Something //Create a graph Created_Graph.PageRank(power_iterations); ## Related products ## C0P3530 Stepik Solution – Stacks&Queues ## SOLVED:CSE205 Assignment #7 ## COP3530 Programming Assignment 1 – Binary Search Tree ## [Solved] COP 3530 Programming Assignment -3: Simplified Page Rank Algorithm INSTANT DOWNLOAD! 100/100 Trustscore on scamadviser.com 10 USD$

• Description
• Reviews (0)

In late 90’s as the number of webpages on the internet were growing exponentially different search engines were trying different approaches to rank the webpages. At Stanford, two computer science PhD students, Sergey Brin and Larry Page were working on the following questions: How can we trust information? Why are some web pages more important than others? Their research led to the formation of the Google search engine. In this programming assignment, you are required to implement a simplified version of the original PageRank algorithm on which Google was built.

Representing the Web as a Graph

The idea that the entire internet can be represented as a graph. Each node represents a webpage and each edge represents a link between two webpages. This graph can be implemented as an Adjacency Matrix or an Adjacency List. Feel free to use any data structure.

Now for the sake of simplicity, we are explaining the assignment in the form of an Adjacency Matrix. We represent the graph in the form of |V|x|V| matrix where |V| is the total number of vertices in the graph. This is mapped to the webpages in the entire internet. Thus, if there is an edge from V i to V j (the from_page points to_page), we have the value in our adjacency matrix M ij = 1 and 0 otherwise.

Core Idea of PageRank

• Important web pages will point to other important webpages.
• Each page will have a score and the results of the search will be based on the page score (called page rank).

Rank(i) = j/out_degree(j) + k/out_degree(k)

Each webpage is thus a node in the directed graph and has incoming edges and outgoing edges. Each node has a rank. According to PageRank, this rank is equally split among the node’s outgoing links and this rank is equal to the sum of the incoming ranks. The rank is based on the indegree (the number of nodes pointing to it) and the importance of incoming node. This is important considering let’s say you create your personal website and have a million links to other pages of importance. If this was not the case and rank used out links, we can easily dupe the algorithm. Therefore, the rank is based on in-links.

In this assignment, you need to compute the rank of the webpages using a Simplified Algorithm explained in the example below.

Line 1 contains the number of lines (n) that will follow and the number of power iterations you need to perform. Each line from

2 to n will contain two URL’s – from_page to_page separated by a space. This means from_page points to the URL to_page.

Print the PageRank of all pages after n powerIterations in ascending alphabetical order of webpage. Also, round off the rank of the page to two decimal places.

## Explanation through a Core Example

google.com maps.com facebook.com ufl.edu ufl.edu google.com ufl.edu gmail.com maps.com facebook.com gmail.com maps.com

Output facebook.com 0.20 gmail.com 0.20 google.com 0.10 maps.com 0.30

ufl.edu 0.20

Step 1: Mapping for Simplicity (Optional but you will need a mechanism to store unique vertices) Use a map/array to map the URL’s with a unique id

Data Structure 1

Step 2: Graph Representation and Page Rank

In page rank, the equation for your graph is given as follows:-

Rank of a Page, r= M.r where,

M is the matrix with values given by the following:

M ij = 1/d j if there is an edge from V j to V i (d j is the outdegree of node j)

For our graph, the adjacency matrix, M will look like:

Step 3: Power iteration, r(t+1)=M.r(t)

This means that a rank of the webpage at time t+1 is equal to the rank of that page at time t multiplied by matrix, M. To achieve this, we create our matrix M based on input. Next, we initialize r(t) which is a matrix of size |V|x1 and consists of the ranks of every webpage. We initialize r(t) to 1/|V|. Next we compute power_iterations based on our input.

1 1 2 3 4 5

1 2 3 4 5 1 1

r(t+1)=r(0+1)=r(1) =M.r(0)= 2 =

M x r(0) = r(1)

In this input case, the number of power_iterations is 2, if it is 1 then return the initializing rank matrix or r(0). If iterations>2, the process repeats where you multiply the matrix, M with the new rank matrix r(t+1) at the next iteration.

Stepik Test Case Two Explanation:- (Power_iteration=3)

r(t+1)=r(1+1)=r(2) =M.r(1)= 2 =

M x r(1) = r(2)

You are allowed to use your own template but make sure your code passes the sample test cases. An example template to think about the problem is :

Class AdjacencyListorMatrix { private:

//Think about what member variables you need to initialize public:

//Think about what helper functions you will need in the algorithm

void AdjacencyListorMatrix::PageRank(int n){ } // prints the PageRank of all pages after n powerIterations in ascending alphabetical order of webpage and rounding rank to two decimal places]

// This class and method are optional. To accept input, you can use this method:

int no_of_lines, power_iterations;

std::string from, to; std::cin >> no_of_lines; std::cin >> power_iterations;

for(int i=0;i< no_of_lines;i++)

{ std::cin>>from; std::cin>>to;

// Do Something

//Create a graph

Created_Graph.PageRank(power_iterations);

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## [Solved] COP3530 Project 2 -AVL and BST Efficiency Comparrison

[solved] cop3530 p0 100/100, [solved] cop3530 programming assignment 2 – hashing- hashing analysis, [solved] c0p3530 stepik solution – stacks&queues, [solved] quiz 11 – graphs, [solved] programming assignment 1 – binary search tree.

#### IMAGES

1. PageRank algorithm: how it works

2. Useful Tricks For Mastering A New Programming Assignment

3. Page Rank algorithm and implementation in Python for Data Science

4. Page Rank algorithm and implementation in Python for Data Science

5. PPT

6. Study of Page Rank Algorithms

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#### COMMENTS

1. Page Rank Algorithm and Implementation

PageRank (PR) is an algorithm used by Google Search to rank websites in their search engine results. PageRank was named after Larry Page, one of the founders of Google. PageRank is a way of measuring the importance of website pages. According to Google:

2. GitHub: Let's build from here · GitHub

The PageRank is\\n\","," \"the ranked order of the pages from the most to the least probable page the surfer will be viewing.\\n\""," ]"," },"," {"," \"cell_type\": \"code\","," \"execution_count\": 20,"," \"metadata\": {},"," \"outputs\": ["," {"," \"name\": \"stdout\","," \"output_type\": \"stream\","," \"text\": ["," \"Populating the interact...

3. pagerank-algorithm · GitHub Topics · GitHub

Star 3.3k Code Issues Pull requests Module for automatic summarization of text documents and HTML pages. python nlp pagerank-algorithm text-extraction reduction summarization html-page summary lsa sumy textteaser summarizer html-extraction html-extractor Updated 2 weeks ago Python ArtistScript / FastTextRank Star 403 Code Issues Pull requests

4. GitHub

The goals of this assignment are to: 1. Understand the PageRank algorithm and how it works in MapReduce. 2. Implement PageRank and execute it on a large corpus of data. 3. Examine the output from running PageRank on Simple English Wikipedia to measure the relative importance of pages in the corpus.

5. vaghelarahul94/Page-Rank-Python-for-Everybody-Coursera ...

Once you have a few pages in the database, you can run Page Rank on the pages using the sprank.py program. You simply tell it how many Page Rank iterations to run.

6. Programming Assignment 3 Instructions

Goal:In this assignment, we will compute PageRank score for the web dataset provided by Google in a programming challenge in a programming constest in 2002. Input Format:The datasets are given in txt. The file format is: Rows from 1 to 4: Metadata. They give information about the dataset and are self-explained.

7. PDF PageRank Project

In this assignment you will implement the PageRank algorithm used for ranking web pages. You will be provided with a small and a large web graph for running PageRank. You will then analyze the performance and stability of the algorithm as you vary its parameters.

8. CS 377P: Programming for Performance

Page-rank Compute page-rank values for all three graphs. Verify the correctness of your implementation using the Wiki graph before running it on the other two graphs. Submission 1. (90 points) Submit (in canvas) your code and all the items listed in the experiments above.

9. page-rank · GitHub Topics · GitHub

Multithreaded crawling of UIC domain, inverted index, page rank, SEO with Context Pseudo-Relevance Feedback ... Lab Assignments of Course Web Mining (CSE-3024) ... Python program that generates the page rank of the Stanford web graph from 2002. python pagerank page-rank page-rank-algorithm Updated Mar 17, 2023; Python;

10. GitHub

Page Rank in Spark Summary Spark is a general-purpose distributed data processing engine that is suitable for use in a wide range of circumstances. In this assignment you will learn to use the PySpark Python API for Spark, and will be implementing a Page Rank algorithm leveraging Spark. A quick overview on Spark:

11. GitHub

PageRank . aka this was interesting.. C implementation of the PageRank algorithm, with and without parallelization. Used as a group project for the High Performance Computing course held at Ca' Foscari University of Venice, master's degree in Computer science. The algorithm is implemented sequentially and then parallelized using the openMP library.. The code

12. GitHub

C# implementation of the PageRank algorithm. Contribute to jeffersonhwang/pagerank development by creating an account on GitHub.

13. Implementing page rank algorithm in Java assignment help

The assignment consists of two parts. The first part requires the implementation of a well-known PageRank algorithm, which calculates page relevance, based on a given webpages graph (set of links between webpages). The algorithm created by our Java assignment help doer takes the input file containing links in the graph and shows the final and ...

14. Implementing Page Rank Algorithm Assignment Help

Need help with Python Assignment Help or Project Help? At Codersarts we offer 1:1 session with expert, Code mentorship, Code mentorship, Course Training, and ongoing development projects. Get help from vetted Machine Learning engineers, mentors, experts, and tutors. Task The goal of this task is to implement a well known page rank algorithm in python for a large network of dataset.

15. Assignment 3: PageRank (Due Date: Thursday November 1st at 23:59pm)

PageRank is the basis of Google's ranking of web pages in search results. Given a directed graph where pages are nodes and the links between pages are edges, the algorithm calculates the likelihood, or rank, that a page will be visited. The rank of a page is determined recursively by the ranks of the pages that link to it.

16. Applied Social Network Analysis in Python

5 videos 1 quiz 1 programming assignment 1 ungraded lab. ... Page Rank, and Hubs and Authorities. You'll learn about the assumptions each measure makes, the algorithms we can use to compute them, and the different functions available on NetworkX to measure centrality. In the assignment, you'll practice choosing the most appropriate centrality ...

17. Page rank algorithm implementation in Java assignment help

Our Java assignment help solvers must read all the necessary web-page data from a given sample file and process with Page Rank algorithm to determine the order of these pages by relevance. Necessary algorithm parameters such as convergence delta, iterations number, etc, are provided.

18. GitHub: Let's build from here · GitHub

I.e. the principal eigenvector of the damped system, using the power iteration method.","# (Normalisation doesn't matter here)","# The functions inputs are the linkMatrix, and d the damping parameter - as defined in this worksheet.","def pageRank (linkMatrix, d) :"," n = linkMatrix.shape [0]"," "," M = d * linkMatrix + (1-d)/n * np.ones ( [n, n]...

19. Request Google's Page-rank Programmatically

Google's PageRank (PR) is a "link analysis algorithm measuring the relative importance" (PR @wikipedia ). The importance of PR nowadays is a lot lower than one or two years ago. Nevertheless, PR is the only ranking value that is public to all audience, which means it's the only factor with some transparency. For those who don't know: a PR of 10 ...

20. COP 3530 Programming Assignment -3: Simplified Page Rank Algorithm

Core Idea of PageRank Important web pages will point to other important webpages. Each page will have a score and the results of the search will be based on the page score (called page rank). Rank (i) = j/out_degree (j) + k/out_degree (k) Each webpage is thus a node in the directed graph and has incoming edges and outgoing edges.

21. Rank (computer programming)

In computer programming, rank with no further specifications is usually a synonym for (or refers to) "number of dimensions"; thus, a two-dimensional array has rank two, a three-dimensional array has rank three and so on. Strictly, no formal definition can be provided which applies to every programming language, since each of them has its own concepts, semantics and terminology; the term may ...

22. COP 3530 Programming Assignment -3: Simplified Page Rank Algorithm

In this programming assignment, you are required to implement a simplified version of the original PageRank algorithm on which Google was built. Representing the Web as a Graph The idea that the entire internet can be represented as a graph. Each node represents a webpage and each edge represents a link between two webpages.

23. [Solved] COP 3530 Programming Assignment -3: Simplified Page Rank

Rank (i) = j/out_degree (j) + k/out_degree (k) Each webpage is thus a node in the directed graph and has incoming edges and outgoing edges. Each node has a rank. According to PageRank, this rank is equally split among the node's outgoing links and this rank is equal to the sum of the incoming ranks.