Search Engine Ranking Simulation Using PageRank Algorithm

Overview

This project implements the PageRank algorithm to simulate how search engines determine the relative importance of webpages based on their link structure.

Using concepts from graph theory and linear algebra, webpages are represented as nodes in a directed graph and transformed into matrix representations for iterative PageRank computation. The project demonstrates how mathematical models can be applied to ranking problems in information retrieval systems.

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Features

• PageRank algorithm implementation
• Directed graph representation of webpages
• Adjacency and stochastic matrix construction
• Google matrix generation using damping factor
• Iterative PageRank computation
• Convergence analysis
• Graph visualization
• Ranking of webpages based on importance

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Concepts Demonstrated

• Linear Algebra
• Graph Theory
• Matrix Representation
• Matrix Multiplication
• Stochastic Matrices
• Eigenvector Approximation
• Iterative Numerical Methods
• Convergence Analysis

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Workflow

Input Dataset
      │
      ▼
Directed Graph
      │
      ▼
Adjacency Matrix
      │
      ▼
Stochastic Matrix
      │
      ▼
Google Matrix
      │
      ▼
Iterative PageRank
      │
      ▼
Final Rankings
      │
      ├────────► Graph Visualization
      └────────► Convergence Analysis

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Dataset

The project uses a simplified website link structure where each webpage links to one or more other webpages.

Example:

Google -> YouTube Gmail Maps Drive
YouTube -> Google
Gmail -> Google Drive
Maps -> Google
Drive -> Google Gmail
Wikipedia -> Google YouTube
Amazon -> Google YouTube
Reddit -> Wikipedia YouTube

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Technologies Used

Technology	Purpose
Python	Core implementation
NumPy	Matrix operations
NetworkX	Graph representation
Matplotlib	Data visualization

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Installation

Install the required dependencies:

pip install numpy networkx matplotlib

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Running the Project

python src/main.py

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Output

The application generates:

• PageRank scores for each webpage
• Ranked list of webpages
• Graph visualization
• Convergence plot

Example:

Google      0.31
YouTube     0.21
Wikipedia   0.14

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Project Structure

Search-Engine-Ranking/
│
├── src/
│   ├── main.py
│   ├── pagerank.py
│   └── ...
│
├── data/
│
├── output/
│   ├── pagerank_graph.png
│   ├── convergence_plot.png
│
└── README.md

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Applications

• Search Engine Ranking
• Network Analysis
• Link Analysis
• Graph Algorithms
• Information Retrieval
• Linear Algebra Applications

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Learning Outcomes

This project demonstrates practical implementation of:

• Graph-based algorithms
• Linear algebra applications
• Matrix computation
• Numerical iterative methods
• Data visualization
• Scientific programming using Python

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Future Enhancements

• Import real web graph datasets
• Interactive network visualization
• Personalized PageRank
• Weighted graph support
• Performance optimization for large datasets
• Web interface for visualization

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Conclusion

This project demonstrates how mathematical concepts such as graph representations, stochastic matrices, and iterative computation can be used to simulate webpage ranking. It provides a practical implementation of the PageRank algorithm while showcasing the application of linear algebra in search engine technology.