The notebook in this repository provides several algorithmic solutions to the PageRank algorithm for computing importance scores on graphs of varying sizes.

This notebook was a deliverable of a project in the course 'Linear Algebra and Optimization' tought on the Bachelor of Data Science at the IT University of Copenhagen.

The notebook begins with a theoretical exercise detailing the matrix representation of a directed graph. One can think of the directed graph as a representation of a web with n pages (nodes) that link (edges) to other pages.

Following the theoretical exercise, four algorithms to compute the PageRank score on a graph are presented:

• The RandomSurfer algorithm
• A simple PageRank algorithm
• An optimized PageRank algorithm
• A graph representation and PageRank algorithm optimized for large graphs

Two graphs were given for this exercise and can be found in the graphs zip-folder:

• p2p-Gnutella08-mod.txt - A medium-sized graph consisting of 6301 nodes and 20777 edges
• bigRandom.txt - A large graph consisting of 199999 nodes and 10011343 edges

• Python 3
• networkX Python library
• scipy Python library