The purpose of this activity is to investigate how the PageRank algorithm behaves in relation to the damping factor when applied to small graphs and certain special graph types. The PageRank algorithm involves the calculation of eigenvalues and eigenvectors of the Google matrix for both directed and undirected graphs. This discussion will focus on all directed graphs with up to four vertices and select special graphs. Our primary objective is to observe how the damping factor influences the dominant eigenvector for each graph and, consequently, how it impacts PageRank. We have calculated PageRank for all the graphs and conducted an analysis, particularly focusing on the effect of the damping factor, denoted as "c," in our discussions. To compute the PageRank algorithm, we constructed a probability matrix for all the graphs and performed the calculations using MATLAB. This process yielded eigenvalues and eigenvectors associated with the Google matrix. The theoretical section of this thesis encompasses the PageRank theory, including essential proofs, theorems, and definitions that serve as foundational elements throughout the thesis. Additionally, we delve into the historical context and practical applications of PageRank. In our study, we present a comparative analysis of the results, specifically examining the impact of a damping factor on the dominant PageRank eigenvector.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:mdh-66992 |
| Date | January 2024 |
| Creators | Edirisingha Pathirannahelage, Chathuranga Ruwan Kumara |
| Publisher | Mälardalens universitet, Akademin för utbildning, kultur och kommunikation |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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