Index

a

  • Adamic‐Adar node 71, 72, 79, 81
  • agglomerative methods 39
  • aggressive cutting strategy 252
  • airline traffic network 151
  • Albert, Reka 5
  • alters 62
  • articulation point 35, 36, 38, 316
  • Asheville, vehicle routing problem in 285–299
  • authority centrality 151–157, 327
    • measures 102
  • authorship graph 167
  • auto insurance, fraud detection in 312–320
  • auto‐relationship 167
  • average degree 8
  • average path length 8
  • average revenue per user (ARPU) 6

b

  • back‐and‐forth approach 111
  • backtracking algorithm 176
  • Barabási, Albert‐László 5
  • Bellman = Ford algorithm 220
  • betweenness centrality 129–136, 316
  • biconnected component 35–38
    • input graph with undirected links 36
    • links table 37
    • nodes table 38
    • results 37
    • summary table 38
  • binary relations 235, 237
  • bipartite graphs 70, 72, 75, 76, 179, 180
  • Boolean functions 90
  • Bott, Helen 4
  • Boykov‐Kolmogorov algorithm 195
  • branch‐and‐bond method 242
  • branch‐and‐bound nodes 252, 253
  • branch‐and‐cut process 251
  • brewing process 265, 266
  • bridges 35
  • brute‐force search algorithm 25

c

  • Call Detail Records (CDRs) xii
  • Capacitated Vehicle Routing Problem (CVRP) 286
  • Carley, Kathleen 5
  • cascade process 320
  • centralities 123 see also network centralities
  • centrality measures 302
  • centrality metrics 299, 316, 322, 325
  • central node 24
  • characteristics of networks 7
  • claims 315
    • nodes and links assigned to 313
    • same participants 313, 314
  • cliques 278
    • of graph 170–176
    • within transportation network 278
  • closeness centrality 124–129
  • cluster coefficient measures 102
  • clustering analysis 316
  • clustering coefficient 7, 8, 10, 121–124
  • coding‐assessment process 113
  • common neighbors node 72, 73, 75
  • community detection 38–58, 316
    • agglomerative methods 39
    • communities’ attributes table 48, 49
    • communities level table 47, 50–53, 55–57
    • communities’ links table 50
    • divisive methods 39
    • FIX option 41, 42
    • to identify fraud events in telecommunications 324–328
    • LINKREMOVALRATIO option 43
    • links table 44, 47, 48
    • Louvain algorithm 39–41, 44, 46, 49, 50, 53, 58
    • MAXITERS option 44
    • nodes table 44, 47, 48, 51, 52, 54–57
    • OUTCOMMUNITY option 45
    • OUTLEVEL option 44
    • overlap table for 47, 49
    • RANDOMFACTOR option 44
    • RANDOMSEED option 44
    • RECURSIVE option 42
    • RESOLUTIONLIST option 42, 46
    • summary results 46, 47
    • TOLERANCE option 44
    • WARMSTART option 42
  • connected components 26–27, 315, 318
    • directed graphs 26, 31, 32, 34
    • input graph with undirected links 27, 30, 33
    • LINKSVAR statement 27
    • output links table for 28–31, 33, 34
    • output nodes table for 28–30, 32–34
    • output results 28, 31, 33
    • output summary table 28, 30, 32–34
    • in proc network 26–33
    • undirected graphs 26, 28, 31
  • connected subgraph 23
  • connector 2–3
  • core 58–64
  • core decomposition 301
  • correlation coefficient 302
  • cosine node 72, 81
  • Cosine similarity 78
  • COVID‐19 outbreaks 271
    • communities based on population movements 301
    • inferred network of cases 305
    • key performance indicators (KPIs) 299, 300, 301
    • network analysis to predict 298, 299–305
    • network centrality measures, locations based on 302
    • population movement and 300
    • risk level locations of all groups 303
    • supervised machine learning models 304
  • customer influence to reduce churn and increase product adoption 320–324
  • customers’ demands 292, 297
  • cut ratio 45
  • cutting plane method 252
  • CVRPSEP package 251
  • cycle algorithm 278, 279
  • cycle enumeration 176–179

d

  • damping factor 144, 146
  • data preparation 298
  • data structure for network analysis and network optimization 13–15
  • decision variable 180
  • degree centrality 102, 162, 169
    • computing 103–110
    • out‐degree and in‐degree 103
    • visualization 110–114
  • degree‐normalized adjacent matrix 150
  • demand‐supply problem 188–194
  • Dengue disease 310, 311
  • density of community 43
  • density of network 7–8
  • depot node 257, 260, 263, 264
  • diameter of network 8
  • Dijkstra’s algorithm 220
  • directed acyclic graph 266
  • directed graphs 6, 26, 60
    • betweenness centrality 130, 133, 134
    • closeness centrality 127–129
    • clustering coefficient centrality 123
    • community detection 40, 41
    • connected components 26, 31, 32, 34
    • cycles 177
    • degree centrality 103, 104, 107
    • to eigenvector centrality 141–143
    • influence centrality 118, 119
    • modularity equation for 40
    • network projection 72
    • node similarity 78, 87, 88, 98
    • PageRank centrality 145
    • path 218
    • reach network 63, 65
    • shortest path 232
    • vehicle routing problem 262, 263, 265
    • with weighted nodes and links. 6
    • traveling salesman problem 247, 248
  • disconnected subgraph 23
  • divisive methods 39
  • dual simplex algorithm 194
  • Durkheim, Émile 4
  • dynamic network analysis 5

e

  • Eglese, Richard W. 251
  • egocentric networks see reach networks
  • ego nodes 62, 64
  • eigenvalue 136, 138, 140, 155
  • eigenvector centrality 136–143
    • computing 137–143
    • directed graph 141–143
    • OUTNODES dataset 140, 141, 143
    • square matrix 136, 137
    • undirected graph 137
  • elementary cycle 239, 240
  • embedding vector space 80
  • ethnographic approach 4
  • Euclidian distance 274, 275, 287, 308
  • Euler Circuit 169
  • Euler, Leonhard 167–168
  • exaggeration 319

f

  • feature extraction 298
  • first order proximity 77, 79, 82
  • fixed costs 250
  • Flood, Merrill 240
  • fraud detection in auto insurance 312–320
  • fraud events, in telecommunications 324–328
  • Function Compiler (FCMP) functions 90, 91

g

  • geo‐network 163
  • Gladwell, Malcolm 3
  • global transportation cost 286
  • Granovetter, Mark Sanford 8
  • graph 23, 24
    • loading and unloading graph 15
    • main 88–93, 96
    • nodes and links 102
  • graph diameter 10
  • graph matching. see pattern matching
  • graphs 167
  • graph theory 1, 5, 26, 102, 167
    • history 167–169
    • minimum cut 199–205
    • node similarity in 77
    • path 208–220

h

  • Hagman, Elizabeth 4
  • Hamiltonian cycle 25, 239, 240
  • Hamilton, Willian Rowan 240
  • harmonic centrality 125
  • heuristic local optimization approach 40
  • hexagons nodes 93, 94
  • history in social studies 4–5
  • homomorphic subgraph 88
  • hub centrality 151–157, 327
  • hub centrality measures 102
  • hybrid approach 163

i

  • in‐degree centrality 103, 104
  • individuals’ attributes 4
  • induced subgraph 23, 24, 63, 89, 91
  • influence
    • network centralities 101
    • network metrics of power and 102–103
  • influence factor 102
  • influential factors 102, 271, 321
  • input dataset 27
  • integer linear programming formulation 250
  • isomorphic subgraph 88
  • isomorphism 25–26
  • iterative method 146, 147, 154

j

  • Jaccard node 72, 78, 81, 85
  • Jacobi‐Davidson algorithm 136, 156

k

  • k‐core decomposition 58–64
  • key performance indicators (KPIs) 299, 300, 301
  • Kirkman, Thomas 240
  • Königsberg bridges 167–169
  • Krackhardt, David 5
  • Kronecker delta 40
  • Kruskal’s algorithm 206

l

m

  • machine learning 1, 39, 101, 102, 157, 298
  • main graph 88–93, 96
  • Markov process 144, 146
  • maximal clique 170
  • maximum network flow
    • in distribution problem 195–199
    • links in 195
  • maximum network flow problem 194–199
  • Milgram, Stanley 10, 11
  • MINCOSTFLOW statement 187
  • minimum‐cost network flow algorithm 185–194
    • in demand‐supply problem 188–194
    • dual values 191
    • for flexible network 194
    • for links 190, 193
    • links and the nodes 187–188
    • LINKSOUTMCNF dataset 189
    • mathematical formulation 187
    • MINCOSTFLOW statement 187
    • for nodes 191
    • reduced cost 189
    • results by proc optnetwork 190
    • transshipment node 186
  • minimum cut 199–205
    • applications 199–200
    • finding 201–205
    • link metric 199–200
    • minimum s‐t cut problem 199, 200, 202, 205
    • nodes and links 200
  • minimum spanning tree algorithm 205–209, 279, 280
  • minimum s‐t cut problem 199, 200, 202, 205
  • minimum weight matching in worker‐task problem 181–185
  • mixed integer linear programming 170
  • mobile carriers 306
  • mobility behavior 299–301, 305, 308
    • spatiotemporal analysis on 305
  • modularity 39, 40, 44, 46, 58, 325
  • Monte Carlo algorithms 240
  • Moreno, Jacob 4–5
  • movement behavior 300
  • Multi Depot Vehicle Routing Problem (MDVRP) 286
  • multilink 14
  • multimodal transportation system 272–285
  • multivariate analysis 326
  • mutually reinforced relationship 154

n

  • negative sampling 80
  • network analysis 12
    • data structure for 13–15
    • options for 15–16
    • to predict COVID‐19 outbreaks 298–305
  • network analytics 12
  • network centralities xii, 271
    • authority centrality 151–157
    • betweenness centrality 129–136
    • calculation by group 157–164
    • closeness centrality 124–129
    • clustering coefficient 121–124
    • degree centrality (see degree centrality)
    • eigenvector centrality 136–143
    • hub centrality 151–157
    • influence centrality 114–121
    • network metrics of power and influence 102–103
    • PageRank centrality 144–151
  • network metrics 58, 123
    • of power and influence 102–103
  • network optimization 1–2, 13, 111, 167–168, 275, 278
    • clique of graph 170–176
    • cycle 176–179
    • data structure for 13–15
    • linear assignment 179–185
    • maximum network flow problem 194–199
    • minimum‐cost network flow algorithmis 185–194
    • minimum cut 199–205
    • minimum spanning tree algorithm 205–209
    • options for 15–16
    • path 208–220
    • in SAS Viya 170
    • shortest path 220–235
    • topological sort 265–268
    • transitive closure 235–240
    • traveling salesman problem 239–249
    • Vehicle Routing Problem (VRP) 249–265
  • NETWORK procedure 13, 14
  • network projection 70–77
  • network simplex algorithm 194
  • network structure 77
  • node filters 91
  • node‐pair filters 91
  • nodes dataset 91
  • NodeSetIn 41, 42
  • node similarity 77–88
    • Adamic‐Adar similarity 79
    • applications 77
    • common neighbors 78, 79
    • computing 82–88
    • Cosine similarity 78
    • in graph theory 77
    • input undirected graph 83
    • Jaccard similarity 78
    • measures 85, 88
    • optimization process 80
    • outcomes 87
    • parallel link weights 79
    • structural role proximity 77
    • vectors for 84
  • NODESVAR statement 254
  • nondeterministic polynomial time problem 249
  • non‐deterministic Turing Machine 25
  • non‐integer linear program 242
  • normalized metrics 131, 133

o

  • objective function 180
  • Open Vehicle Routing Problem (OVRP) 286
  • optimal beer kegs distribution 285–298
  • optimal tour 240–249, 272–285
  • optimization process 80
  • OPTLP 194
  • OPTNETWORK procedure 13, 14
  • Origin‐Destination (OD) matrix 306
  • outlier analysis 314, 316, 324, 326

p

  • PageRank centrality 102, 144–151
  • parallel label propagation 39
  • parallel label propagation algorithm 40, 41, 43, 46, 52–54
  • PARALLELLABELPROP algorithm 160
  • Paris, traveling salesman (TSP) problem 271–285
    • cliques within 278
    • closest stations to locations to visit 284
    • final optimal tour 285
    • minimum spanning tree algorithm 280
    • paths within transportation network 281
    • pattern match algorithm 282
    • shortest path 282
  • path 208–220, 239
    • directed input graph with weighted links 211
    • finding 211–220
    • fixed sink node 215–217
    • fixed source node 214–217
    • for links 213, 219
    • LINKSVAR statement 210
    • for nodes 214, 217, 220
    • sink node 208–210
    • source node 208–210
    • within transportation network 281
  • pattern matching 88
    • links table 96, 97
    • main graph 88–93, 96
    • nodes table 91–97
    • outcome 96, 98
    • query graphs 88–90, 92, 93, 97
    • results by proc network 94
    • searching for subgraphs matches 91–97
    • within transportation network 282
  • PCANS Model 5
  • population movement index 300
  • post analysis procedures 298
  • power law distribution 309
  • power method 136, 147, 148, 156
    • network metrics of 102–103
  • primal simplex algorithm 194
  • proc optnetwork 170, 173
  • product adoption event 321–323
  • projected network see network projection
  • properties of networks 7–8
  • public transportation system 272

q

r

  • random graphs 9–12
  • reach networks 62–70
    • applications 62–63
    • counts table 69
    • DIGRAPH forces proc network 65
    • for directed graph 65
    • ego nodes 64
    • links table 67, 68
    • NODESSUBSET option 64
    • nodes table 67
    • in proc network 63, 64, 66
  • real‐world applications in network science 271
    • customer influence to reduce churn and increase product adoption 320–324
    • fraud detection in auto insurance 312–320
    • multimodal transportation system 272–285
    • optimal beer kegs distribution 285–298
    • urban mobility in Metropolitan cities 306–312
  • recursive methods 41, 49, 58, 325
  • recursive partitioning process 54
  • Régie Autonome des Transports Parisiens (RAPT) 272, 276
  • regular graphs 9, 10
  • relevant links 325
  • relevant nodes 325
  • resolution 325

s

  • SAS Studio 110, 111, 114
  • SAS Viya xii, 13, 170
  • SAS Viya Network Analytics features 298
  • scale‐free network 5
  • second order proximity 77, 79, 80
  • self‐link 14
  • set theory 23
  • shelter‐in‐place policies 305
  • shortest path 220–235, 272
    • auxiliary weight 221
    • finding 225–235
    • NODESVAR statement 222
    • source‐sink nodes 221, 222
    • within transportation network 282
  • Simmel, George 4, 11
  • single clique 174, 175
  • singleton graphs 19
  • sink node 86, 208–210
  • small world concept 8–11
  • social and political networks 35
  • social behavior studies 5
  • social containment measures 303, 304
  • social containment policies 301
  • social network analysis 9, 25
    • history 3–5
    • overall process 324
  • social structures 314, 318, 320, 321, 325
  • social studies, history in 4–5
  • Société Nacionale des Chemins de fer Français (SNCF) 272
  • source node 86, 208–210
  • spatiotemporal analysis 305
  • SQL procedure 91
  • square matrix 136, 137
  • star graph 24
    • central node 24
  • star network 319
  • statistical models 1, 39, 101, 102, 298
  • stochastic gradient descent algorithm 80
  • structural role proximity 77
  • subgraph isomorphism problem 25, 88
  • subgraphs 24, 60
    • by links selection 24
    • nodes 23
    • by removing nodes 24
  • subnetwork analysis 23
    • biconnected component 35–38
    • community detection 38–58
    • connected components 26–27
    • core 58–62
    • isomorphism 25–26
    • network projection 70–76
    • node similarity 77–88
    • reach networks 62–70
  • summary statistics 16–21
    • for les misérables network 17–21
  • supdem variable 190–191
  • supernode 41, 42
  • supervised machine learning models, to predict COVID‐19 outbreaks 298–305
  • supervised models 1
  • supply chain processes 35

t

  • telecommunications xii, 1, 6, 41, 103, 115, 120, 162, 271, 320
    • community detection to identify fraud events in 324–328
    • minimum‐cost network flow algorithm 269
    • minimum spanning tree algorithm 205
  • The New York Times 4–5
  • Time Dependent Vehicle Routing Problem (TDVRP) 286
  • topological ordering 265–268
  • topological sort 265–268
  • TOPOLOGICALSORT (TOPSORT) statement 266
  • topology 7, 52, 53, 58, 102, 169, 272, 303, 325
  • trajectory matrix 306
  • transitive closure 235–240
  • Transitive Closure algorithm 272
  • transportation agencies 310
  • transshipment node 186
  • traveling salesman problem (TSP) 169, 239–249

u

  • undirected graph 6
    • betweenness centrality 130–132
    • biconnected component 35, 36
    • closeness centrality 125, 126
    • clustering coefficient 8
    • clustering coefficient centrality 121, 122
    • community detection 39, 41
    • connected components 26, 28, 31
    • degree centrality 103–104
    • to eigenvector centrality 137, 141
    • influence centrality 116
    • node similarity 78
    • PageRank centrality 147
    • shortest path 231, 232
    • transitive closure 238, 239
    • traveling salesman problem 246
  • union‐find algorithm 26
  • unipartite graph 70
  • univariate analysis 316
  • unloading the graph 15
  • unnormalized metrics 131
  • unsupervised models 1
  • urban mobility in Metropolitan cities 306–312
    • Dengue disease 310, 311
    • distance traveled by subscribers 310
    • nodes and links 308
    • presumed domiciles and workplaces 307
    • traffic and movements on weekdays and weekends 311
    • traffic volume by day 309
    • types of 306

v

  • variable warm 54
  • vector node similarity 82
  • vehicle routing problem (VRP) 249–265
    • applications 250
    • in Asheville 285–298
    • binary variable 250
    • capacity 252, 257
    • centralized depot node 252
    • depot node 257, 260, 263, 264
    • directed graph 262, 263, 265
    • high maximum capacity 259
    • high vehicle maximum capacity 261, 262
    • integer linear programming formulation 250
    • low maximum capacity 258
    • nodes and demands 260
    • optimal vehicle routes for delivery problem 253–265
    • options for 251–253
    • in proc optnetwork 251, 257
    • routes and sequence of nodes 260, 264
    • undirected input graph 253, 255, 257
  • Vehicle Routing Problem with Heterogenous Fleets (HFVRP) 286
  • Vehicle Routing Problem with Pickup and Delivery (VRPPD) 286
  • Vehicle Routing Problem with Profits (VRPPs) 286
  • Vehicle routing Problem with Time Window (VRPTW) 286
  • viral effect of purchasing 323
  • vis.js. 111
  • visual analytics 110, 120, 299
  • VRP see vehicle routing problem (VRP)

w

  • Watts, Duncan 10
  • weighted degree 108
  • Wellman, Beth 4
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