what-when-how
In Depth Tutorials and Information
Chapter 4
AnalyzingSociotechnical
Networks:ASpectrum
Perspective
Xintao Wu, Xiaowei Ying, and Leting Wu
Contents
4.1 Introduction...............................................................................................72
4.1.1 Contribution...................................................................................73
4.1.2 Organization...................................................................................73
4.2 Spectral versus Real Characteristics............................................................74
4.3 Spectrum-Based Graph Randomness Analysis ...........................................76
4.3.1 Graph Spectral Geometry ...............................................................76
4.3.2 Spectrum-Based Randomness Framework ......................................80
4.3.2.1 Edge Nonrandomness:
R
(
u
,
v
) ..........................................81
4.3.2.2 Node Nonrandomness:
R
(
u
) .............................................81
4.3.2.3 Graph Nonrandomness
RG
and Relative
Nonrandomness
R
G
∗
.........................................................83
4.4 Spectral Analysis of Graph Perturbation ....................................................87
4.4.1 Graph Characteristics versus Perturbation: An Illustrating
Example..........................................................................................87
4.4.2 heoretical Analysis of Spectral Perturbation..................................88
4.4.3 Spectrum-Preserving Randomization .............................................94
4.5 Conclusion and Future Work ...................................................................100
Acknowledgments .............................................................................................100
References ......................................................................................................... 101
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