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 Complex Networks

A Networking and Signal Processing Perspective

Contents

Preamble

  • Preface

  • Acknowledgments

  • About the Authors

  • About the Cover

Chapter 1: Introduction

  • Complex Networks

  • Types of Complex Networks

  • Benefits of Studying Complex Networks

  • Challenges in Studying Complex Networks

  • What This Book Offers

  • Organization of the Book

  • Support Materials Available for Instructors

  • Summary

Chapter 2: Graph Theory Preliminaries

  • Introduction

  • Graphs

  • Matrices Related to a Graph

  • Basic Graph Metrics

  • Basic Graph Definitions and Properties

  • Types of Graphs

  • Other Important Measures for Graphs

  • Graph Pathfinding Algorithms

  • Summary

  • Exercises

Chapter 3: Introduction to Complex Networks

  • Major Types of Complex Networks

  • Complex Network Metrics

  • Community Detection in Complex Networks

  • Entropy in Complex Network

  • Random Networks

  • Open Research Issues

  • Summary

  • Exercises

Chapter 4: Small-World Networks

  • Introduction

  • Milgram’s Small-World Experiment

  • Characteristics of Small-World Networks

  • Real-World Small-World Networks

  • Creation and Evolution of Small-World Networks

  • Capacity-Based Deterministic Addition of New Links

  • Creation of Deterministic Small-World Networks

  • Anchor Points in a String Topology Small-World Network

  • Heuristic Approach-Based Deterministic Link Addition

  • Routing in Small-World Networks

  • Capacity of Small-World Networks

  • Open Research Issues

  • Summary

  • Exercises

Chapter 5: Scale-Free Networks

  • Introduction

  • Characteristics of Scale-Free Networks

  • Real-World Scale-Free Networks

  • Scale-Free Network Formation

  • Preferential Attachment–Based Scale-Free Network Creation

  • Fitness-Based Scale-Free Network Creation

  • Varying Intrinsic Fitness-Based Scale-Free Network Creation

  • Optimization-Based Scale-Free Network Creation

  • Scale-Free Network Creation with Exponent 1

  • Greedy Global Decision–Based Scale-Free Network Creation

  • Deterministic Scale-Free Network Creation

  • Open Research Issues

  • Summary

  • Exercises

Chapter 6: Small-World Wireless Mesh Networks

  • Introduction

  • Classification of Small-World Wireless Mesh Networks

  • Creation of Random Long-Ranged Links

  • Small-World Based on Pure Random Link Addition

  • Small-World Based on Euclidean Distance

  • Realization of Small-World Networks Based on Antenna Metrics

  • Algorithmic Approaches to Create Small-World Wireless Mesh Networks

  • Gateway-Router-Centric Small-World Network Formation

  • Creation of Deterministic Small-World Wireless Mesh Networks

  • Creation of Non-Persistent Small-World Wireless Mesh Networks

  • Non-Persistent Routing in Small-World Wireless Mesh Networks

  • Qualitative Comparison of Existing Solutions

  • Open Research Issues

  • Summary

  • Exercises

Chapter 7: Small-World Wireless Sensor Networks

  • Introduction

  • Small-World Wireless Mesh Networks vs. Small-World Wireless Sensor Networks

  • Why Small-World Wireless Sensor Networks?

  • Challenges in Transforming WSNs to SWWSNs

  • Types of Long-Ranged Links for SWWSNs

  • Approaches for Transforming WSNs to SWWSNs

  • SWWSNs with Wired LLs

  • Open Research Issues

  • Summary

  • Exercises

Chapter 8: Spectra of Complex Networks

  • Introduction

  • Spectrum of a Graph

  • Adjacency Matrix Spectrum of a Graph

  • Adjacency Matrix Spectra of Complex Networks

  • Laplacian Spectrum of a Graph

  • Laplacian Spectra of Complex Networks

  • Network Classification Using Spectral Densities

  • Open Research Issues

  • Summary

  • Exercises

Chapter 9: Signal Processing on Complex Networks

  • Introduction to Graph Signal Processing

  • Comparison between Classical and Graph Signal Processing

  • The Graph Laplacian as an Operator

  • Quantifying Variations in Graph Signals

  • Graph Fourier Transform

  • Generalized Operators for Graph Signals

  • Applications

  • Windowed Graph Fourier Transform

  • Open Research Issues

  • Summary

  • Exercises

Chapter 10: Graph Signal Processing Approaches

  • Introduction

  • Graph Signal Processing Based on Laplacian Matrix

  • DSPG Framework

  • DSPG Framework Based on Weight Matrix

  • DSPG Framework Based on Directed Laplacian

  • Comparison of Graph Signal Processing Approaches

  • Open Research Issues

  • Summary

  • Exercises

Chapter 11: Multiscale Analysis of Complex Networks

  • Introduction

  • Multiscale Transforms for Complex Network Data

  • Crovella and Kolaczyk Wavelet Transform

  • Random Transform

  • Lifting-Based Wavelets

  • Two-Channel Graph Wavelet Filter Banks

  • Spectral Graph Wavelet Transform

  • Spectral Graph Wavelet Transform Based on Directed Laplacian

  • Diffusion Wavelets

  • Open Research Issues

  • Summary

  • Exercises

Appendices

  • Vectors and Matrices

  • Classical Signal Processing

  • Analysis of Locations of Anchor Points

  • Asymptotic Behavior of Functions

  • Relevant Academic Courses and Programs

  • Relevant Journals and Conferences

  • Relevant Datasets and Visualization Tools

  • Relevant Research Groups

Epilogue

  • Notation

  • Acronyms

  • Bibliography

  • Index