Index
ACC ratio, 280
ACES, 151
Acyclic graph, 29
Acyclicity, 29
Adjacency matrix, 19
Algebraic connectivity, 325
Algebraic signal processing, 394
Algorithm-based addition, 234
Contact based, 234
GA based, 235
SCR based, 235
All pair shortest path, 52
American football network, 190
Anchor points, 134
ANFC, 128
Antenna metric-based addition, 230
Randomized beamforming, 231
Transmission power, 230
Transmission power and beamforming, 233
APL optimization, 208
APL to base station, 25
APSP, 52
Assortative mixing, 68
ATPL, 256
Average clustering coefficient, 23, 62, 108
Average flow capacity enhancement using small-world characteristics, 151
Average neighbor degree, 23, 62
Average network flow capacity, 128
Average path length, 24, 62, 108
Average path length to BS, 280
Average transmission path length, 256
Bandlimited graph signal, 358
Barabási-Albert model, 196, 198
Betweenness centrality, 66
Bipartite graph, 41
Blocks, 28
Bridges, 28
Call blocking probability, 255
Capacity of small-world networks, 166
Capacity-based link addition Max-flow min-cut, 125
Cartesian product, 39
CBP, 255
CCD, 140
Centrality, 63
Betweenness centrality, 66
Closeness centrality, 64
Degree centrality, 63
Eigenvector centrality, 68
GFT centrality, 68
Graph centrality, 67
Cheeger constant, 48
Cheeger inequality, 324
Circuit, 27
CKWT, 432
Classical convolution product, 363, 471
Classical downsamplers and upsamplers, 474
Classical filter banks, 474
Classical Fourier transform, 472
Classical signal processing, 345, 471
Classical two-channel filter bank, 475
Classical vs. graph signal processing, 345
Classical windowed Fourier transform, 476
Clique number, 48
Closeness centrality, 64
Closeness centrality disparity, 140
Co-authorship network, 194
Community detection, 70
Conflict graph transform based, 72
CTCD, 72
Modularity maximization, 71
Surprise maximization, 72
Comparison of graph signal processing approaches, 415
Competitive multiscaling, 200
Complement graph, 17
Complete graph, 42
Complex networks, 59
ACC, 62
AND, 62
APL, 62
Average clustering coefficient, 62
Average neighbor degree, 62
Average path length, 62
Centrality, 63
Betweenness centrality, 66
Closeness centrality, 64
Degree centrality, 63
Eigenvector centrality, 68
GFT centrality, 68
Graph centrality, 67
Community detection, 70
Conflict graph transform based, 72
Modularity maximization, 71
Surprise maximization, 72
Degree correlation, 68
Assortative mixing, 68
Disassortative mixing, 68
Degree distribution, 63
Major types, 59
Metrics, 62
Network diameter, 62
Network resistance distance, 70
Node criticality, 69
Random networks, 60
Scale-free networks, 61
Small-world networks, 60
Conflict graph transform–based community detection, 72
Connected graphs, 27
Contact-based routing, 234
Continuous time wavelet transform, 477
CPAN network, 194
Crovella and Kolaczyk wavelet transform, 432
CTCD, 72
Cut set, 29
Cut-vertices, 28
DAG, 29
DAS, 289
Data-mule-based LL creation, 248
Degree centrality, 63
Degree correlation, 68
Assortative mixing, 68
Disassortative mixing, 68
Degree distribution, 63, 113, 182
Degree matrix, 20
Degree-based LL addition, 294
Depth-first search, 30
Deterministic approach, 213
Deterministic link addition, 130
MaxBC, 134
MaxCC, 134
MinAEL, 133
MinAPL, 131
Near-optimal, 132
Optimal, 131
Sequential, 132
Deterministic LL creation, 245
Exhaustive search based, 247
Heuristic approach based, 247
DFS, 30
DFS number, 30
DFT, 347
DFT vs GFT, 347
Diffusion wavelets, 454
Dijkstra’s shortest path algorithm, 49
Directed acyclic graph, 29
Directed acyclicity test, 30
Directed augmentation, 289
Directed graph, 14
Directed Laplacian matrix, 22
Directed random model, 289
Directivity, 14
Dirichlet form, 351
Disassortative mixing, 68
Discrete Fourier transform, 347, 473
Discrete time Fourier transform, 472
Diseasome network, 116
Dolphin network, 114
Downsampling, 439
DRM-SWWSN, 289
DSPG framework, 395
Directed Laplacian based, 405
Weight matrix based, 397
Dual graph, 33
Edge connectivity, 28
Edge-cut, 29
Eigenfunctions, 471
Eigenvector centrality, 68
Euclidean distance–based LL addition, 229
Euler’s formula, 33
Eulerian circuit, 35
Eulerian graph, 35
Eurosis web mapping network, 192
Exhaustive search, 247
Fielder vector, 325
Five-color Theorem, 35
Friendship network, 114
GA-based routing, 235
GAGS, 241
GAS, 238
Gateway mesh router, 221
Gateway-aware greedy LL addition strategy, 241
Gateway-aware LL addition strategy, 238
Gateway-router-based LL addition, 237
G-APL, 237
Multi-gateway router, 242
LM-GAS, 244
M-GAS, 243
Qualitative comparison, 245
Single gateway-router, 237
GAGS, 241
GAS, 238
RAS, 237
Gateway-router-based routing, 237
G-APL, 237
Multi-gateway router, 242
LM-GAS, 244
M-GAS, 243
Single gateway-router, 237
GAGS, 241
GAS, 238
RAS, 237
Generalized operators, 361
GFT, 351
GFT centrality, 68
GFT-C, 68
Graph, 15
Graph centrality, 67
Graph coloring, 34
Graph diameter, 26
Graph filtering, 361
Graph Fourier transform, 351, 400, 409
Graph Fourier transform based on directed Laplacian, 409
Graph Fourier transform centrality, 375
Graph frequency, 354
Graph harmonics, 355
Graph matrices, 18
Graph metrics, 23
Graph product, 38
Graph QMF, 445
Graph quadrature mirror filter banks, 445
Graph signal, 345
Graph signal processing, 342
Graph spectral distribution, 113, 182
Graph spectrum, 349
Adjacency matrix spectrum, 312
Laplacian matrix spectrum, 322
Graph types, 41
Graph volume, 26
Greedy decision, 208
Greedy reasoning–based model, 198
Grid topology, 285
GSP based on Laplacian, 394
Hamiltonian circuit, 36
Hamiltonian graph, 36
Heuristic approach, 247
Heuristics-based link addition, 139
MaxCCD, 140
SDLA, 146
HgSWWSN, 296
Homogeneous model, 296
Hub nodes, 180
ID-SWWSNs, 296
Impulse response, 471
Incidence matrix, 19
Induced subgraph, 16
Inhibition distance–based model, 296
Isomorphic graph, 32
Isomorphism, 32
Jazz musicians network, 190
Kirchoff’s matrix tree theorem, 43
Königsberg bridge problem, 13
Kronecker product, 39
Kruskal’s MST algorithm, 44
Laplacian matrix, 20
Les Misérables network, 114
Lifting-based wavelets, 437
Line Graph, 45
Linear graph filters, 395
Link creation
Capacity based, 125
Deterministic link addition, 130
MaxBC, 134
MaxCC, 134
MinAEL, 133
MinAPL, 131
Near-optimal, 132
Optimal, 131
Sequential, 132
Euclidean distance based, 123
Heuristics-based link addition, 139
MaxCCD, 140
SDLA, 146
Pure random addition, 120
Rewiring, 118
LL saturation, 281
LM-GAS, 244
Load balancing, 256
Load-aware LL creation, 249
Load-balanced multi-gateway-aware LL addition strategy, 244
Long-ranged link addition, 228
Euclidean distance based, 229
Pure random, 228
LTI filters, 471
M-GAS, 243
Marvel Universe network, 194
Max-flow min-cut, 125
Max-flow min-cut theorem, 38
MaxCap, 128
Maximum flow capacity, 128
Mesh client, 221
Mesh router, 221
Milgram’s experiment, 109
Minimum spanning tree, 44
Modularity maximization, 71
MST, 44
MST algorithm, 44
Multi-gateway-aware LL addition strategy, 243
Multi-gateway-router-based LL addition, 242
LM-GAS, 244
M-GAS, 243
Multigraph, 15
Multiscale transforms on graphs, 430
Spectral domain designs, 431
Vertex domain designs, 431
Network classification, 224, 335
Network creation, 117
Network flow, 36
Network resistance distance, 70
Newman-Watts model, 287
Node criticality, 69
Nonpersistent LL creation, 248
Data-mule-based LL creation, 248
LNPR, 252
Load-aware LL creation, 249
Nonpersistent routing, 252
Nonpersistent routing, 252
Normalized Laplacian matrix, 21
NW-SWWSN, 287
Optimization, 203
Optimization-based model, 197
Paley-Wiener space, 358
Path, 27
Planar graph, 32
Planarity, 32
Political blog, 192
Popularity and similarity, 203
Preferential attachment, 196, 198
Protein-protein interaction network, 194
Pseudograph, 15
Pure random addition, 120, 228
Degree distribution, 121
Random LL addition strategy, 237
Random LL creation, 225
Random model, 286
Random transform, 435
Randomized beamforming, 231
WFB, 231
Wireless flow betweenness, 231
RAS, 237
Real-world small-world networks, 114
Regular graph, 41
Regular topology, 281
Ring topology, 283
RM-SWWSN, 286
Routing
Adaptive decentralized routing algorithm, 161
Decentralized routing algorithm, 160
Lookahead routing algorithm, 165
Nonpersistent routing, 252
Routing in small-world networks, 159
Scale-free networks, 177
APL optimization, 208
Barabási-Albert model, 196, 198
Competitive multiscaling, 200
Degree distribution, 182
Deterministic approach, 213
Graph spectral distribution, 182
Greedy decision, 208
Greedy reasoning–based model, 198
Hub nodes, 180
Network diameter, 180
Optimization, 203
Optimization-based model, 197
Popularity and similarity, 203
Preferential attachment, 196, 198
Real-world examples, 183
Air traffic network, 191
Air traffic networks, 184
American football network, 190
Co-authorship network, 194
CPAN network, 194
EuroSiS web mapping network, 192
Jazz musicians network, 190
Marvel Universe network, 194
Political blog, 192
Protein-protein interaction network, 194
Sociology networks, 183
Twitter crawl network, 194
US Air-97 network, 191
Word adjacency network, 188
World trade networks, 188
Yeast network, 194
Zachary’s karate club network, 186
Rewiring, 206
Small-world properties, 180
SDLA, 146
Sequential deterministic LL addition, 146
Shift invariance, 395
Shortest path algorithm, 49
Single gateway-router-based LL addition, 237
GAGS, 241
GAS, 238
RAS, 237
Small-world characteristics, 110, 223
Small-world cooperative routing, 235
Small-world networks, 107
ACC, 108
ACES, 151
Anchor points
Locations, 136
Observations, 138
Significance, 135
ANFC, 128
APL, 108
Average clustering coefficient, 108
Average flow capacity enhancement using small-world characteristics, 151
Average network flow capacity, 128
Average path length, 108
Capacity, 166
LL addition, 168
Rewiring, 167
Degree distribution, 113
Diseasome network, 116
Dolphin network, 114
Friendship network, 114
Graph spectral distribution, 113
Les Misérables network, 114
MaxCap, 128
Maximum flow capacity, 128
Milgram’s experiment, 109
Network creation, 117
Anchor points, 134
Capacity-based addition, 125
Deterministic link addition, 130
Euclidean distance–based addition, 123
Heuristics-based link addition, 139
Pure random addition, 120
Rewiring, 118
Real-world small-world networks, 114
Routing, 159
Adaptive decentralized routing algorithm, 161
Decentralized routing algorithm, 160
Lookahead routing algorithm, 165
Six degrees of separation, 109
Small-world characteristics, 110
Degree distribution, 113
Graph spectral distribution, 113
Western state power grid network, 116
Small-world properties, 180
Small-world wireless mesh networks, 221
Architecture, 222
Deterministic LL creation, 245
Exhaustive search based, 247
Heuristic approach based, 247
Gateway mesh router, 221
Mesh client, 221
Mesh router, 221
Network classification, 224
Nonpersistent LL creation, 248
Data-mule-based LL creation, 248
LNPR, 252
Load-aware LL creation, 249
Nonpersistent routing, 252
Qualitative comparison, 257
Random LL creation, 225
Addition, 228
Rewiring, 227
Small-world characteristics, 223
Small-world wireless sensor networks, 267
Nsat, 281
ACC ratio, 280
APLB, 280
Average path length to BS, 280
Classification, 279
DAS, 289
Degree based, 294
Directed augmentation, 289
Directed random model, 289
DRM-SWWSN, 289
Grid topology, 285
HgSWWSN, 296
Homogeneous model, 296
ID-SWWSNs, 296
Inhibition distance–based model, 296
Kleinberg’s model, 288
LL saturation, 281
Metrics, 279
Newman-Watts model, 287
NW-SWWSN, 287
Random model, 286
Regular topology, 281
Ring topology, 283
RM-SWWSN, 286
String topology, 281
Variable rate adaptive modulation, 292
VRAM-SWWSN, 292
Wired model, 299
Sociology networks, 183
Spanning tree, 43
Spectra of complex networks
Adjacency matrix spectra, 316
Laplacian matrix spectra, 331
Spectral bisection, 325
Spectral folding, 443
Spectral graph clustering, 327
Spectral graph wavelet transform, 446
Spectral graph wavelet transform
Based on directed Laplacian, 450
Spectral graph wavelets, 446
Spectrogram, 476
String topology, 281
Strong product, 40
Subgraph, 16
Surprise maximization, 72
SWWMNs, 221
Architecture, 222
Deterministic LL creation, 245
Exhaustive search based, 247
Heuristic approach based, 247
Gateway mesh router, 221
Mesh client, 221
Mesh router, 221
Network classification, 224
Nonpersistent LL creation, 248
Data-mule-based LL creation, 248
LNPR, 252
Load-aware LL creation, 249
Nonpersistent routing, 252
Qualitative comparison, 257
Random LL creation, 225
Addition, 228
Rewiring, 227
Small-world characteristics, 223
SWWSNs, 267
Nsat, 281
ACC ratio, 280
APLB, 280
Average path length to BS, 280
Classification, 279
DAS, 289
Degree based, 294
Directed augmentation, 289
Directed random model, 289
DRM-SWWSN, 289
Grid topology, 285
HgSWWSN, 296
Homogeneous model, 296
ID-SWWSNs, 296
Inhibition distance–based model, 296
Kleinberg’s model, 288
LL saturation, 281
Metrics, 279
Newman-Watts model, 287
NW-SWWSN, 287
Random model, 286
Regular topology, 281
Ring topology, 283
RM-SWWSN, 286
String topology, 281
Variable rate adaptive modulation, 292
VRAM-SWWSN, 292
Wired model, 299
Traceable graph, 36
Transmission power, 230
Transmission power and beamforming, 233
Traversability, 35
Tree, 42
Twitter crawl network, 194
Two-channel graph wavelet filter banks, 439
Unweighted graph, 15
US Air-97 network, 191
Variable rate adaptive modulation, 292
Variations in graph signals, 349
Vertex connectivity, 28
Vertex indexing, 358
Vertex-Cut, 29
VRAM-SWWSN, 292
Walk, 27
Wavelet generating kernels, 448
Weight matrix, 18
Weighted graph, 15
Western state power grid network, 116
WFB, 231
Windowed graph Fourier transform, 381
Wired model, 299
Wireless flow betweenness, 231
Word adjacency network, 188
World trade network, 188
Yeast network, 194
Zachary’s karate club network, 186