Wiley-VCH - Bücher | November 2002 | Handbook of Graphs and Networks

	Bücher \| November 2002 \| Handbook of Graphs and Networks \| Inhaltsverzeichnis

Bücher

	Soeben erschienen
	Titelsuche
	Featured Sites
	Unterhaltung

Zeitschriften

Elektronische Medien

	Contents


	Preface	V
	List of contributors	XIV
1	Mathematical results on scale-free random graphs (Béla Bollobás and Oliver M. Riordan)	1
1	Introduction	1
1.2	Classical models of random graphs	2
1.3	Results for classical random graphs	4
1.4	The Watts-Strogatz `small-world' model	5
1.5	Scale-free models	6
1.6	The Barabási-Albert model	7
1.7	The LCD model and G⁽ⁿ⁾_m	9
1.8	The Buckley-Osthus model	11
1.9	The copying model	12
1.10	The Cooper-Frieze model	13
1.11	Directed scale-free graphs	15
1.12	Clustering coefficient and small subgraphs	17
1.13	Pairings on [0, 1]and the diameter of the LCD model	22
1.14	Robustness and vulnerability	24
1.15	The case [0, 1]: plane-oriented recursive trees	27
1.16	Conclusion	32
	References	32
2	Random graphs as models of networks (Mark E. J. Newman)	35
2.1	Introduction	35
2.2	Random graphs with specified degree distributions	40
2.3	Probability generating functions	45
2.3.1	Properties of generating functions	46
2.3.2	Examples	46
2.4	Properties of undirected graphs	47
2.4.1	Distribution of component sizes	47
2.4.2	Mean component size	50
2.4.3	Above the phase transition	51
2.5	Properties of directed graphs	53
2.5.1	Generating functions	54
2.5.2	Results	54
2.6	Networks with clustering	56
2.7	Models defined on random graphs	58
2.7.1	Network resilience	58
2.7.2	Epidemiology	61
2.7.3	The SIR model	62
2.7.4	Solution of the SIR model	63
2.8	Summary	65
	References	65
3	Emergence of scaling in complex networks (Albert-László Barabási)	69
3.1	Introduction	69
3.2	Network models	70
3.2.1	Random networks	70
3.2.2	Scale-free networks	70
3.2.3	Scale-free model	73
3.3	Fitness model and Bose-Einstein condensation	75
3.4	The Achilles' Heel of complex networks	76
3.5	A deterministic scale-free model	79
3.6	Outlook	81
3.7	Acknowledgments	82
	References	82
4	Structural properties of scale-free networks (Reuven Cohen, Shlomo Havlin, and Daniel ben-Avraham)	85
4.1	Introduction	85
4.1.1	Random graphs	85
4.1.2	Scale-free networks	86
4.2	Small and Ultra-small worlds	87
4.2.1	Diameter of scale-free networks	88
4.2.2	Minimal graphs and lower bound	88
4.2.3	The general case of random scale-free networks	89
4.3	Percolation	92
4.3.1	Random breakdown	92
4.3.2	Percolation critical threshold	93
4.3.3	Generating functions	95
4.3.4	Intentional attack	96
4.3.5	Critical exponents	97
4.3.6	Fractal dimension	100
4.4	Percolation in directed networks	101
4.4.1	Threshold	102
4.4.2	Critical exponents	103
4.5	Efficient immunization strategies	104
4.5.1	Acquaintance immunization	105
4.6	Summary and outlook	106
	References	107
5	Epidemics and immunization in scale-free networks (Romualdo Pastor-Satorras and Alessandro Vespignani)	111
5.1	Introduction	111
5.2	Computers and epidemiology	112
5.3	Epidemic spreading in homogeneous networks	114
5.4	Real data analysis	116
5.5	Epidemic spreading in scale-free networks	118
5.5.1	Analytic solution for the Barabási-Albert network	119
5.5.2	Finite size scale-free networks	122
5.6	Immunization of scale-free networks	123
5.6.1	Uniform immunization	124
5.6.2	Targeted immunization	125
5.7	Conclusions	127
	References	128
6	Cells and genes as networks in nematode development and evolution (Ralf J. Sommer)	131
6.1	Introduction	131
6.2	Nematode developmental biology: studying processes at a cellular level	132
6.3	Nematode Vulva formation as a case study	132
6.4	Nematode collections	136
6.5	Cellular networks: how cells change their function	136
6.5.1	Evolution of vulva position	136
6.5.2	Evolution of vulval cell fate specification	136
6.6	Genetic networks: how genes change their function	139
6.6.1	Evolution of lin-39 function	139
6.6.2	Evolution of mab-5 function	141
6.7	Conclusion	142
	References	142
7	Complex networks in genomics and proteomics (Ricard V. Solé and Romualdo Pastor-Satorras)	145
7.1	Introduction	145
7.2	Cellular networks	148
7.2.1	Two-gene networks	149
7.2.2	Random networks	150
7.3	Three interconnected levels of cellular nets	153
7.4	Small world graphs and scale-free nets	154
7.5	Scale-free proteomes: gene duplication models	157
7.5.1	Mean-field rate equation for the average connectivity	157
7.5.2	Rate equation for the node distribution n_k	159
7.5.3	Numerical simulations	162
7.6	Discussion	164
	References	164
8	Correlation profiles and motifs in complex networks (Sergei Maslov, Kim Sneppen, and Uri Alon)	168
8.1	Introduction	168
8.2	Randomization algorithm: Constructing the proper null model	172
8.3	Correlation profiles: Yeast molecular networks and the Internet	177
8.4	Network motifs: Transcriptional regulation in E. coli	189
8.5	Discussion: What it may all mean?	194
	References	196
9	Theory of interacting neural networks (Wolfgang Kinzel)	199
9.1	Introduction	199
9.2	On-line training	200
9.3	Generalisation	201
9.4	Time series prediction and generation	203
9.5	Self-interaction	206
9.6	Agents competing in a closed market	207
9.7	Synchronisation by mutual learning	208
9.8	Cryptography	210
9.9	Conclusions	213
	References	216
10	Modelling food webs (Barbara Drossel and Alan J. McKane)	218
10.1	Introduction	218
10.2	Basic properties of food webs	221
10.3	Static models	226
10.4	Dynamic models	227
10.4.1	Two-species models	228
10.4.2	Generalized dynamical equations	230
10.4.3	The complexity-stability debate	232
10.5	Assembly models and evolutionary models	235
10.5.1	Toy models	235
10.5.2	Species assembly models	236
10.5.3	Evolutionary models	238
10.6	Conclusions	241
	References	242
11	Traffic networks (Kai Nagel)	248
11.1	Introduction	248
11.2	Dynamics on networks	250
11.2.1	The four step process and static assignment	250
11.2.2	Simple link dynamics and the queue model	252
11.2.3	Virtual reality micro-simulations	253
11.2.4	CA implementations of virtual reality micro-simulations	255
11.2.5	Traffic in networks	258
11.3	Particles are intelligent	260
11.3.1	Route generation	260
11.3.2	Activity generation	261
11.3.3	Housing, land use, freight, life style, et al	261
11.3.4	Day-to-day learning, feedback, and relaxation	261
11.3.5	Within-day re-planning	262
11.3.6	Individualization of knowledge	263
11.3.7	State of the art	263
11.4	Distributed computing and the network of interactions	264
11.4.1	Distributed computing of the traffic micro-simulation	265
11.4.2	Distributed computing of plans generation	267
11.5	Outlook: Dynamics of networks	268
11.6	Conclusion	268
	References	269
12	Economic networks (Alan Kirman)	273
12.1	Introduction	273
12.2	Economics and sociology	274
12.3	The economic consequences of networks	275
12.4	Fixed network: stochastic interaction	278
12.5	Random graphs and networks	280
12.6	Emerging networks	281
12.7	The strategic formation of networks	282
12.8	Emerging random graphs	283
12.9	The identification problem	291
12.10	Conclusion	292
	References	293
13	Local search in unstructured networks (Lada A. Adamic, Rajan M. Lukose, Bernardo A. Huberman)	295
13.1	Introduction	295
13.2	Search in power-law random graphs	297
13.2.1	Intuition	297
13.2.2	Random walk search	298
13.2.3	Search utilizing high degree nodes	301
13.3	Simulation	303
13.4	Comparison with Poisson distributed graphs	306
13.5	Gnutella	308
13.6	Path finding	310
13.7	Shortening the shortest path	312
13.7.1	Iterative deepening	313
13.8	Adaptive search	314
13.9	Conclusion	315
	References	316
14	Accelerated growth of networks (Sergei N. Dorogovtsev and Jose F. F. Mendes)	318
14.1	Acceleration	318
14.2	Reasons for acceleration	321
14.3	Degree distributions of networks	321
14.3.1	Types of degree distribution	321
14.3.2	Power-law degree distribution	324
14.4	General relations for accelerated growth	326
14.5	Scaling relations for accelerated growth	328
14.6	Degree distributions produced by acceleration	329
14.6.1	Model for < 2	329
14.6.2	Model for > 2	330
14.6.3	Dynamically induced accelerated growth	330
14.6.4	Partial copying of edges and multifractality	330
14.7	Evolution of the Word Web	331
14.8	Wealth distribution in evolving societies	336
14.8.1	Stable (stagnating) societies	337
14.8.2	Developing and degrading societies	337
	References	339
15	Social percolators and self organized criticality (Gérard Weisbuch and Sorin Solomon)	342
15.1	Introduction	342
15.2	Social percolation	343
15.2.1	Simple models	343
15.3	Adjustment meta-dynamics	346
15.3.1	Slow adjustment	346
15.3.2	Fast adjustment	347
15.4	Conclusions	351
	References	353
16	Graph theory and the evolution of autocatalytic networks (Sanjay Jain and Sandeep Krishna)	355
16.1	Introduction	355
16.2	Graph theory and autocatalytic sets .	357
16.2.1	Directed graphs and their adjacency matrices	357
16.2.2	Autocatalytic sets	363
16.3	A dynamical system on a fixed graph	366
16.3.1	Attractors of equation (16.1)	368
16.4	Graph dynamics	375
16.5	Self Organization	377
16.5.1	The random phase	378
16.5.2	The growth phase	381
16.5.3	The organized phase	384
16.6	Catastrophes and recoveries in the organized phase	384
16.6.1	Catastrophes, core-shifts and a classification of proximate causes	389
16.6.2	Recoveries	391
16.6.3	Correlation between graph theoretic nature of perturbation and its short and long term impact	392
16.7	Concluding remarks	392
	References	394
	Index	396

	Bestellen
	Online-Ausgabe
	Inhaltsverzeichnis
	Kurzbeschreibung
	Langtext
	Besprechungen
	Autoreninformation
	Sitz der Autoren


	Low Temperature Plasmas Fundamentals, Technologies and Techniques Econophysics An Introduction Geothermal Energy Systems Exploration, Development, and Utilization
	[mehr >>]


	Propellants, Explosives, Pyrotechnics Plasma Processes and Polymers
[mehr>>]


	Weiner, Irving B. / Craighead, W. Edward The Corsini Encyclopedia of Psychology 495,- Euro gültig bis 3. Mai 2010
	[mehr Angebote >>]

Seite empfehlen RSS-Feeds Druckversion

©2010 Wiley-VCH Verlag GmbH & Co. KGaA - Betreiber
http://www.wiley-vch.de - mailto: info@wiley-vch.de
Datenschutz