Complex networks: a networking and signal processing perspective
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
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Boston
Prentice Hall
[2018]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxxi, 537 Seiten Diagramme |
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| 100 | 1 | |a Manoj, B. S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex networks |b a networking and signal processing perspective |c B. S. Manoj ; Abhishek Chakraborty ; Rahul Singh |
| 264 | 1 | |a Boston |b Prentice Hall |c [2018] | |
| 300 | |a xxxi, 537 Seiten |b Diagramme | ||
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| 700 | 1 | |a Chakraborty, Abhishek |e Verfasser |4 aut | |
| 700 | 1 | |a Singh, Rahul |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | Contents
Preface xvii
Acknowledgments xxi
About the Authors xxvii
About the Cover xxxi
1 Introduction 1
1.1 Complex Networks 1
1.2 Types of Complex Networks 3
1.3 Benefits of Studying Complex Networks 5
1.3.1 Modeling and Characterizing Complex Physical World
Systems 6
1.3.2 Design of New and Efficient Physical World Systems 6
1.3.3 Development of Solutions to Complex Real-World Problems 7
1.3.4 Enhancing Biomedical Research through Molecular
Network Modeling 7
1.3.5 Network Medicine 7
1.3.6 Neutralizing Antisocial Networks 7
1.3.7 Enhanced Social Science Research through Social Networks 8
1.4 Challenges in Studying Complex Networks 8
1.5 What This Book Offers 9
1.6 Organization of the Book 9
1.6.1 Suggested Navigation for Contents of the Book 11
1.7 Support Materials Available for Instructors 12
1.8 Summary 12
2 Graph Theory Preliminaries 13
2.1 Introduction 13
2.2 Graphs 15
2.2.1 Subgraphs 16
2.2.2 Complement of a Graph 17
• • • Contents
Vlll
2.3 Matrices Related to a Graph 18
2.3.1 Weight Matrix 18
2.3.2 Adjacency Matrix 19
2.3.3 Incidence Matrix 19
2.3.4 Degree Matrix 20
2.3.5 Laplacian Matrix 20
2.4 Basic Graph Metrics 23
2.4.1 Average Neighbor Degree 23
2.4.2 Average Clustering Coefficient 23
2.4.3 Average Path Length 24
2.4.4 Average Edge Length 26
2.4.5 Graph Diameter and Volume 26
2.5 Basic Graph Definitions and Properties 27
2.5.1 Walk, Path, and Circuits 27
2.5.2 Connectivity 27
2.5.3 Acyclicity 29
2.5.4 Isomorphism 32
2.5.5 Planarity 32
2.5.6 Colorability 34
2.5.7 Traversability 35
* . . 2.5.8 Network Flows 36
2.5.9 Product Graphs 38
2.6 Types of Graphs 41
2.6.1 Regular Graph 41
2.6.2 Bipartite Graphs 41
2.6.3 Complete Graphs 42
2.6.4 Trees i 42
2.6.5 Line Graph 45
i 2.6.6 Conflict Graphs 46
2.7 Other Important Measures for Graphs 48
-• 2.7.1. Cheeger Constant 48
2.7.2 Clique Number 48
2.8 Graph Pathfinding Algorithms 49
2.8.1 Dijkstra s Shortest Path Algorithm 49
2.8.2 All-Pair Shortest Path Algorithm 52
2.9 Summary 53
Exercises . , 54
3 Introduction to Complex Networks 59
3.1 Major Types of Complex Networks 59
: 3.1.1 Random Networks 60
3.1.2 Small-World Networks 60
3.1.3 Scale-Free Networks 61
... 3.2 Complex Network Metrics 62
3.2.1 Average Neighbor Degree 62
Contents ix
3.2.2 Average Path Length 62
3.2.3 Network Diameter 62
3.2.4 Average Clustering Coefficient 62
3.2.5 Degree Distribution 63
3.2.6 Centrality Metrics 63
3.2.7 Degree-Degree Correlation in Complex Networks 68
3.2.8 Node Criticality 69
3.2.9 Network Resistance Distance 70
3.3 Community Detection in Complex Networks 70
3.3.1 Modularity Maximization 71
3.3.2 Surprise Maximization 72
3.3.3 Conflict Graph Transformation-Based Community Detection 72
3.4 Entropy in Complex Network 84
3.4.1 Network Entropy 84
3.4.2 Nodal Degree Entropy 85
3.4.3 Link Length Variability Entropy 86
3.4.4 Link Influence Entropy 86
3.5 Random Networks 96
3.5.1 Evolution of Random Networks 96
3.5.2 Erdos-Renyi Random Network Model 96
3.5.3 Properties of Random Networks 97
3.6 Open Research Issues % 100
3.7 Summary - 101
Exercises 102
4 Small-World Networks 107
4.1 Introduction 107
4.2 Milgram s Small-World Experiment 109
4.3 Characteristics of Small-World Networks 110
4.4 Real-World Small-World Networks A 114
4.5 Creation and Evolution of Small-World Networks 117
4.5.1 Rewiring of Existing Links 118
4.5.2 Pure Random Addition of New LLs 120
4.5.3 Euclidean Distance-Based Addition of New Links 123
4.6 Capacity-Based Deterministic Addition of New Links 125
4.6.1 Max-Flow Min-Cut Theorem 125
4.6.2 Link Addition Based on Maximum Flow Capacity Strategy 128
4.7 Creation of Deterministic Small-World Networks 130
4.7.1 Link Addition Based on Minimum APL 131
4.7.2 Link Addition Based on Minimum AEL 133
4.7.3 Link Addition Based on Maximum BC 134
4.7.4 Link Addition Based on Maximum CC 134
4.8 Anchor Points in a String Topology Small-World Network 134
4.8.1 Significance of Anchor Points 135
4.8.2 Locations of Anchor Points 136
X
Contents
4.9 Heuristic Approach-Based Deterministic Link Addition 139
4.9.1 Maximum Closeness Centrality Disparity 140
4.9.2 Sequential Deterministic LL Addition 146
4.9.3 Average Flow Capacity Enhancement Using Small-World
Characteristics 151
4.10 Routing in Small-World Networks 159
4.10.1 The Decentralized Routing Algorithm 160
4.10.2 The Adaptive Decentralized Routing Algorithm 161
4.10.3 The Lookahead Routing Algorithm 165
4.11 Capacity of Small-World Networks 166
4.11.1 Capacity of Small-World Networks with Rewiring of
Existing NLs 167
4.11.2 Capacity of Small-World Networks with LL Addition 168
4.12 Open Research Issues 168
4.13 Summary 169
Exercises 171
5 Scale-Free Networks
5.1 Introduction
5.1.1 What Does Scale-Free Mean?
5.2 Characteristics of Scale-Free Networks
5.3 Real-World Scale-Free Networks
5.3.1 The Author Citation Networks
5.3.2 The Autonomous Systems in the Internet
5.3.3 The Air Traffic Networks
5.3.4 Identification of Scale-Free Networks
5.4 Scale-Free Network Formation
5.4.1 Scale-Free Network Creation by Preferential Attachment
5.4.2 Scale-Free Network Creation by Fitness-Based Modeling
5.4.3 Scale-Free Network Creation by Varying Intrinsic Fitness
5.4.4 Scale-Free Network Creation by Optimization
5.4.5 Scale-Free Network Creation with Exponent 1
5.4.6 Scale-Free Network Creation with Greedy Global Decision
Making 198
5.5 Preferential Attachment-Based Scale-Free Network Creation 198
5.5.1 Barabasi-Albert (BA) Network Model 199
5.5.2 Observations and Discussion 200
5.6 Fitness-Based Scale-Free Network Creation 200
5.6.1 Fitness-Based Network Model 201
5.6.2 Observations and Discussion 202
5.7 Varying Intrinsic Fitness-Based Scale-Free Network Creation 202
5.7.1 Varying Intrinsic Fitness-Based Network Model 203
5.7.2 Observations and Discussion 203
5.8 Optimization-Based Scale-Free Network Creation 203
5.8.1 Observations and Discussion 205
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Contents
xi
5.9 Scale-Free Network Creation with Exponent 1
5.9.1 Scale-Free Network Creation with Rewiring
5.9.2 Observations and Discussion
5.10 Greedy Global Decision-Based Scale-Free Network Creation
5.10.1 Greedy Global LL Addition
5.10.2 Observations on Greedy Global Decision-Based Scale-Free
Network
5.11 Deterministic Scale-Free Network Creation
5.11.1 Deterministic Scale-Free Network Model
5.11.2 Observations on Deterministic Scale-Free Network Creation
5.12 Open Research Issues
5.13 Summary
Exercises
6 Small-World Wireless Mesh Networks
6.1 Introduction
6.1.1 The Small-World Characteristics
6.1.2 Small-World Wireless Mesh Networks
6.2 Classification of Small-World Wireless Mesh Networks
6.3 Creation of Random Long-Ranged Links
6.3.1 Random LL Creation by Rewiring the Normal Links
6.3.2 Random LL Creation by Addition of New Links
6.4 Small-World Based on Pure Random Link Addition
6.5 Small-World Based on Euclidean Distance
6.6 Realization of Small-World Networks Based on Antenna Metrics
6.6.1 LL Addition Based on Transmission Power
6.6.2 LL Addition Based on Randomized Beamforming
6.6.3 LL Addition Based on Transmission Power and
Beamforming
6.7 Algorithmic Approaches to Create Small-World Wireless Mesh
Networks
6.7.1 Contact-Based LL Creation
6.7.2 Genetic Algorithm-Based LL Addition
6.7.3 Small-World Cooperative Routing-Based LL Addition
6.8 Gateway-Router-Centric Small-World Network Formation
6.8.1 Single Gateway-Router-Based LL Addition
6.8.2 Multi-Gateway-Router-Based LL Addition
6.9 Creation of Deterministic Small-World Wireless Mesh Networks
6.9.1 Exhaustive Search-Based Deterministic LL Addition
6.9.2 Heuristic Approach-Based Deterministic LL Addition
6.10 Creation of Non-Persistent Small-World Wireless Mesh Networks
6.10.1 Data-Mule-Based LL Creation
6.10.2 Load-Aware Long-Ranged Link Creation
6.11 Non-Persistent Routing in Small-World Wireless Mesh Networks
6.11.1 Load-Aware Non-Persistent Small-World Routing
6.11.2 Performance Evaluation of LNPR Algorithm
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Contents
* 6.12 Qualitative Comparison of Existing Solutions 257
6.13 Open Research Issues 260
6.14 Summary 261
Exercises 263
7 Small-World Wireless Sensor Networks 267
7.1 Introduction 267
7.2 Small-World Wireless Mesh Networks vs. Small-World Wireless
Sensor Networks 269
7.3 , Why Small-World Wireless Sensor Networks? 271
7.4 Challenges in Transforming WSNs to SWWSNs 275
7.5 Types of Long-Ranged Links for SWWSNs 277
7.6 Approaches for Transforming WSNs to SWWSNs 278
7.6.1 Classification of Existing Approaches 279
7.6.2 Metrics for Performance Estimation 279
7.6.3 Transforming Regular Topology WSNs to SWWSNs 281
7.6.4 Random Model Heterogeneous SWWSNs 286
7.6.5 Newman-Watts Model-Based SWWSNs 287
7.6.6 Kleinberg Model-Based SWWSNs 288
7.6.7 Directed Random Model-Based SWWSNs 289
7.6.8 Variable Rate Adaptive Modulation-Based SWWSNs 292
7.6.9 Degree-Based LL Addition for Creating SWWSNs 294
7.6.10 Inhibition Distance-Based LL Addition for Creating
SWWSNs 296
7.6.11 Homogeneous SWWSNs 296
7.7 SWWSNs with Wired LLs 299
7.8 Open Research Issues 301
7.9 Summary 304
Exercises 305
8 Spectra of Complex Networks 309
8.1 Introduction 309
8.2 Spectrum of a Graph 310
: 8.3 Adjacency Matrix Spectrum of a Graph 312
8.3.1 Bounds on the Eigenvalues 313
8.3.2 Adjacency Matrix Spectra of Special Graphs 313
8.4 Adjacency Matrix Spectra of Complex Networks 316
8.4.1 Random Networks 317
8.4.2 Random Regular Networks 318
8.4.3 Small-Wprld Networks . 319
8.4.4 Scale-Free Networks 321
8.5 Laplacian Spectrum of a Graph 322
8.5.1 Bounds on the Eigenvalues of the Laplacian 323
8.5.2 Bounds on the Eigenvalues of the Normalized Laplacian 324
8.5.3 Matrix Tree Theorem 324
Contents
• • *
xm
8.5.4 Laplacian Spectrum and Graph Connectivity 325
8.5.5 Spectral Graph Clustering 327
8.5.6 Laplacian Spectra of Special Graphs 328
8.6 Laplacian Spectra of Complex Networks 331
8.6.1 Random Networks 331
8.6.2 Random Regular Networks 332
8.6.3 Small-World Networks 332
8.6.4 Scale-Free Networks 334
8.7 Network Classification Using Spectral Densities 335
8.8 Open Research Issues 335
8.9 Summary 336
Exercises 337
f
9 Signal Processing on Complex Networks 341
9.1 Introduction to Graph Signal Processing 341
9.1.1 Mathematical Representation of Graph Signals 345
9.2 Comparison between Classical and Graph Signal Processing 345
9.2.1 Relationship between GFT and Classical DFT 347
9.3 The Graph Laplacian as an Operator 348
9.3.1 Properties of the Graph Laplacian 348
9.3.2 Graph Spectrum ; , 349
9.4 Quantifying Variations in Graph Signals 349
9.5 Graph Fourier Transform 351
9.5.1 Notion of Frequency and Frequency Ordering 354
9.5.2 Bandlimited Graph Signals 358
9.5.3 Effect of Vertex Indexing 358
9.6 Generalized Operators for Graph Signals 361
9.6.1 Filtering 361
9.6.2 Convolution 363
9.6.3 Translation v 365
9.6.4 Modulation 366
9.7 Applications 367
9.7.1 Spectral Analysis of Node Centralities 367
9.7.2 Graph Fourier Transform Centrality 375
9.7.3 Malfunction Detection in Sensor Networks 379
9.8 Windowed Graph Fourier Transform 381
9.8.1 Example of WGFT 383
9.9 Open Research Issues 383
9.10 Summary 385
Exercises 386
10 Graph Signal Processing Approaches 393
10.1 Introduction , 393
10.2 Graph Signal Processing Based on Laplacian Matrix 394
10.3 DSPg Framework 394
10.3.1 Linear Graph Filters and Shift Invariance 395
XIV
Contents
10.4 DSPg Framework Based on Weight Matrix 397
10.4.1 Shift Operator 397
10.4.2 Linear Shift Invariant Graph Filters 398
10.4.3 Total Variation 399
10.4.4 Graph Fourier Transform 400
10.4.5 Frequency Response of LSI Graph Filters 404
10.5 DSPg Framework Based on Directed Laplacian 405
10.5.1 Directed Laplacian 405
10.5.2 Shift Operator 406
10.5.3 Linear Shift Invariant Graph Filters 407
10.5.4 Total Variation 408
10.5.5 Graph Fourier Transform Based on Directed Laplacian 409
10.5.6 Frequency Response of LSI Graph Filters 415
10.6 Comparison of Graph Signal Processing Approaches 415
10.7 Open Research Issues 416
10.8 Summary 417
Exercises 419
11 Multiscale Analysis of Complex Networks 429
11.1 Introduction 429
11.2 Multiscale Transforms for Complex Network Data 430
11.2.1 Vertex Domain Designs 431
11.2.2 Spectral Domain Designs 431
11.3 Crovella and Kolaczyk Wavelet Transform 432
11.3.1 CK Wavelets 432
11.3.2 Wavelet Transform 433
11.3.3 Wavelet Properties 434
11.3.4 Examples 434
11.3.5 Advantages and Disadvantages 435
11.4 Random Transform 435
11.4.1 Advantages and Disadvantages 437
11.5 Lifting-Based Wavelets 437
11.5.1 Splitting of a Graph into Even and Odd Nodes 437
11.5.2 Lifting-Based Transform 438
11.6 Two-Channel Graph Wavelet Filter Banks 439
11.6.1 Downsampling and Upsampling in Graphs 439
11.6.2 Two-Channel Graph Wavelet Filter Banks 443
11.6.3 Graph Quadrature-Mirror Filterbanks 445
11.6.4 Multidimensional Separable Wavelet Filter Banks for
Arbitrary Graphs 445
11.7 Spectral Graph Wavelet Transform 446
11.7.1 Matrix Form of SGWT 447
11.7.2 Wavelet Generating Kernels 448
11.7.3 An Example of SGWT / 448
11.7.4 Advantages and Disadvantages 449
Contents
XV
11.8 Spectral Graph Wavelet Transform Based on Directed Laplacian
11.8.1 Wavelets
11.8.2 Wavelet Generating Kernel
11.8.3 Examples
11.9 Diffusion Wavelets
11.9.1 Advantages and Disadvantages
11.10 Open Research Issues
11.11 Summary
Exercises
A Vectors and Matrices
A.l Vectors and Norms
A.1.1 Orthogonal and Orthonormal Vectors
A.1.2 Linear Span of a Set of Vectors
A.2 Matrices
A.2.1 Trace of a Matrix y
A.2.2 Matrix Vector Mutiplication
A.2.3 Column Space, Null Space, and Rank of a Matrix
A.2.4 Special Matrices
A.3 Eigenvalues and Eigenvectors
A.3.1 Characteristic Equation
A.3.2 Eigenspaces
A. 3.3 Eigenvalue Multiplicity
A.4 Matrix Diagonalization
A.5 Jordan Decomposition ■
A.6 Spectral Density
A.7 Wigner s Semicircle Law
A. 8 Gershgorin s Theorem
B Classical Signal Processing
B. l Linear Time Invariant Filters
B. 1.1 Impulse Response and Convolution
B.l.2 Eigenfunctions
B.2 Fourier Transform
B.2.1 Continuous-Time Fourier Transform
B.2.2 Discrete-Time Fourier Transform
B.2.3 Discrete Fourier Transform
B.3 Digital Filter Banks
B.3.1 Downsampler and Upsampler
B.4 Two-Channel Filter Bank
B.5 Windowed Fourier Transform
B.5.1 Spectrogram
B.6 Continuous-Time Wavelet Transform
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C Analysis of Locations of Anchor Points
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XVI
Contents
D Asymptotic Behavior of Functions 485
D.l Big Oh (£ (•)) Notation 485
D.2 Big Omega (Q(*)) Notation 486
D. 3 Big Theta (0(*)) Notation 486
E Relevant Academic Courses and Programs 489
E. l Academic Courses on Complex Networks * 489
E.2 Online Courses on Complex Networks 491
E. 3 Selective Academic Programs on Complex Networks 492
F Relevant Journals and Conferences 493
El List of Top Journals in Complex Networks 493
F. 2 List of Top Conferences in Complex Networks 495
G Relevant Datasets and Visualization Tools 499
G. l Relevant Dataset Repositories 499
v G.2 Relevant Graph Visualization and Analysis Tools 500
H Relevant Research Groups 503
H. l Other Important Resources 506
Notation , 507
Acronyms 509
Bibliography 513
Index 529
/
|
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| author | Manoj, B. S. Chakraborty, Abhishek Singh, Rahul |
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| indexdate | 2024-07-10T07:59:05Z |
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| open_access_boolean | |
| owner | DE-92 DE-739 DE-1050 DE-898 DE-BY-UBR |
| owner_facet | DE-92 DE-739 DE-1050 DE-898 DE-BY-UBR |
| physical | xxxi, 537 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Prentice Hall |
| record_format | marc |
| spelling | Manoj, B. S. Verfasser aut Complex networks a networking and signal processing perspective B. S. Manoj ; Abhishek Chakraborty ; Rahul Singh Boston Prentice Hall [2018] xxxi, 537 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Komplexes System (DE-588)4114261-5 gnd rswk-swf Netzwerk (DE-588)4171529-9 gnd rswk-swf Netzwerk (DE-588)4171529-9 s Komplexes System (DE-588)4114261-5 s DE-604 Chakraborty, Abhishek Verfasser aut Singh, Rahul Verfasser aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030075291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manoj, B. S. Chakraborty, Abhishek Singh, Rahul Complex networks a networking and signal processing perspective Komplexes System (DE-588)4114261-5 gnd Netzwerk (DE-588)4171529-9 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4171529-9 |
| title | Complex networks a networking and signal processing perspective |
| title_auth | Complex networks a networking and signal processing perspective |
| title_exact_search | Complex networks a networking and signal processing perspective |
| title_full | Complex networks a networking and signal processing perspective B. S. Manoj ; Abhishek Chakraborty ; Rahul Singh |
| title_fullStr | Complex networks a networking and signal processing perspective B. S. Manoj ; Abhishek Chakraborty ; Rahul Singh |
| title_full_unstemmed | Complex networks a networking and signal processing perspective B. S. Manoj ; Abhishek Chakraborty ; Rahul Singh |
| title_short | Complex networks |
| title_sort | complex networks a networking and signal processing perspective |
| title_sub | a networking and signal processing perspective |
| topic | Komplexes System (DE-588)4114261-5 gnd Netzwerk (DE-588)4171529-9 gnd |
| topic_facet | Komplexes System Netzwerk |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030075291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT manojbs complexnetworksanetworkingandsignalprocessingperspective AT chakrabortyabhishek complexnetworksanetworkingandsignalprocessingperspective AT singhrahul complexnetworksanetworkingandsignalprocessingperspective |