Index
SYMBOLS
A
Absorbing state, 267
Adjacency matrix, 23
Admissible control, 285
Admissible trajectory, 285
ALOHANET, 9
Aperiodic Markov chain, 267
ARPANET, 6
Arrival process, 262
Autonomous linear ODE, 257
Autonomous ODE, 254
Average path length, 24
B
Birth--death process, 269
Botnet, 34
C
Calculus of variations, 289
Centrality, 24
Chapman-Kolmogorov equations, 267
Clique potentials, 120
Clustering coefficient, 24
Cognitive radio network, 12
Complex network, 18
Computational complexity, 186
Computer virus, 12
Connected network, 19
Connectible networks, 217
Connectivity, 24
Continuous-time Markov chain, 268
Control inputs, 285
Controllability, 288
D
DDoS attacks, 34
Dead state, 37
Differential equation, 289
Differential, 253
Diffusion processes, 29
Discrete-time Markov chains, 266
DoS attacks, 34
Dynamic Programming, 309
E
Epidemic threshold, 50
Epidemics, 44
Equilibrium distribution, 268
Ergodic chain, 267
Ergodic state, 267
Exposed state, 59
Extremal, 290
Extremum, 290
Extremum of functional, 290
F
First-order ODE, 254
Fundamental Lemma of Calculus of Variations, 290
Fundamental Theorem of Calculus of Variations, 290
G
General epidemic model, 48
General solution, 257
Generalized epidemic model, 59
Gibbs Random Field, 118
Gibbs sampling, 120
Graph, 23
GRF, 118
Growth, 26
H
Hamilton--Jacobi--Bellman (HJB) equation, 309
Hamiltonian function, 296
Hammersley–Clifford theorem, 120
Homogeneous linear ODE, 256
Homogeneous Markov chain, 267
Homogeneous Markov process, 268
I
IEEE 802.11 standard, 9
Increment of function, 289
Infected state, 37
Information dissemination, 210
Interarrival times, 263
J
Jacobian matrix, 258
K
Kermack-McKendrick model, 48
L
Little's law, 265
M
Malware, 12
Markov chain, 266
Markov Random Field, 118
Measure, 256
Memoryless property, 266
Minimum control-effort, 299
Minimum-time problems, 298
Monte Carlo algorithm, 120
MRF, 118
N
Network, 16
Network churn, 98
Network formation, 17
Network Science, 21
Non-propagative infection model, 31
Norton equivalent, 75
Null recurrent state, 267
O
Observability, 288
One-step transition probabilities, 267
Optimal control problem, 286
Optimal control, 286
Ordinary differential equation, 253
P
Partial differential equations, 253
Particular solution, 257
Partition function, 119
Passive immunity, 59
Pontryagin's Minimum Principle, 297
Potential function, 120
Power-law networks, 26
Propagation, 31
Propagation process, 31
Propagative infection model, 31
Q
Queuing, 261
Queuing network, 277
Queuing system, 262
R
Random Field, 117
Random graph, 24
Random walk, 63
Recurrent state, 267
Regular graph, 24
Removed state, 37
S
Scale-free network, 25
Separable, 255
Service process, 262
Service times, 263
Shortcut edges, 25
Simple epidemic model, 45
Simulated annealing, 122
Small-world network, 25
Social Network Analysis, 18
Sojourn time, 268
Spreading, 31
Spreading process, 31
Spyware, 34
State diagram, 267
State transition rates, 268
State variables, 285
Strength, 24
Susceptible state, 37
Sweep, 129
Systems of ODEs, 253
T
TCP/IP protocol, 6
Temperature, 119
Temporal dynamics, 253
Transient state, 267
Transition matrix, 268
V
Variation of function, 289
Variational approach, 296
Virtually saturated network, 224
W
Wireless complex networks, 4
WLAN, 9
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