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
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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

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