Graph Laplacians For Directed Networks With Applications To Centrality Measures Open Access

Guo, Yiwen (2017)

Permanent URL: https://etd.library.emory.edu/concern/etds/1g05fc448?locale=en
Published

Abstract

This thesis introduces a new approach to centrality measures by using the non- normalized graph Laplacians. It then compares and contrasts this approach with other existing techniques through small-scale and large-scale examples. Finally, it gives the conclusion and discusses some limitations.

Table of Contents

1 Introduction 4

2 Graph Theory 9

2.1 BasicConcepts ........................... 9

2.2 GraphLaplacians ....................... 12

2.2.1 Symmetric Laplacian Via A Bipartite Graph Model . . . . 13

2.2.2 NonsymmetricLaplacians ................. 16

3 Centrality Measures 22

3.1 Existing Techniques For Centrality Measures . . . . . . . . . . . 23

3.1.1 PageRank.......................... 23

3.1.2 HITS ............................ 23

3.1.3 The Dominant Eigenvector Approach . . . . . . . . . . . 24

3.2 ANewApproachToCentralityMeasure . . . . . . . . . . . . . . 25

4 Experiments And Comparison 28

4.1 Small-scale Graphs ......................... 28

4.2 Larger Graphs............................ 34

5 Conclusion And Discussion 43

About this Honors Thesis

Rights statement
  • Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
School
Department
Degree
Submission
Language
  • English
Research field
Keyword
Committee Chair / Thesis Advisor
Committee Members
Last modified

Primary PDF

Supplemental Files