Graph Laplacians For Directed Networks With Applications To Centrality Measures Open Access
Guo, Yiwen (2017)
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
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