Preface ix

Chapter 1. Introduction 1

1.1 A brief history of the study of networks 1

1.2 The "new" science of networks 4

1.3 Overview of the volume 8

Chapter 2: Historical developments 9

Chain-links, F. Karinthy 21

Connectivity of random nets, R. Solomonoff and A. Rapoport 27

On the evolution of random graphs, P. Erdo os and A. Rényi 38

Contacts and influence, I. de S. Pool and M. Kochen 83

An experimental study of the small world problem, J. Travers and S. Milgram 130

Networks of scientific papers, D. J. de S. Price 149

Famous trails to Paul Erd½ os, R. de Castro and J. W. Grossman 155

Chapter 3: Empirical Studies 167

Diameter of the world-wide web, R. Albert, H. Jeong, and A.-L. Barabási 182

Graph structure in the web, A. Broder et al. 183

On power-law relationships of the internet topology, M. Faloutsos, P. Faloutsos, and C. Faloutsos 195

Classes of small-world networks, L.A.N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley 207

The large-scale organization of metabolic networks, H. Jeong et al. 211

The small world of metabolism, A. Wagner and D. Fell 215

Network motifs: Simple building blocks of complex networks, R. Milo et al. 217

The structure of scientific collaboration networks, M. E. J. Newman 221

The web of human sexual contacts, F. Liljeros et al. 227

Chapter 4: Models of networks 229

4.1 Random graph models 229

A critical point for random graphs with a given degree sequence, M. Molloy and B. Reed 240

A random graph model for massive graphs, W. Aiello, F. Chung, and L. Lu 259

Random graphs with arbitrary degree distributions and their applica-tions, M.E.J. Newman, S. H. Strogatz, and D. J. Watts 269

4.2 The small-world model 286

Collective dynamics of 'small-world' networks, D. J. Watts and S. H. Strogatz 301

Small-world networks: Evidence for a crossover picture, M. Barthélémy and L.A.N. Amaral 304

Comment on'Small-world networks: Evidence for crossover picture', A. Barrat, 1999 308

Scaling and percolation in the small-world network model, M.E.J. New-man and D. J. Watts 310

On the properties of small-world networks, A. Barrat and M. Weigt, 2000 321

4.3 Models of scale-free networks 335

Emergence of scaling in random networks, A.-L. Barabási and R. Albert 349

Structure of growing networks with preferential linking, S. N. Dorogov-tsev, J. F. F. Mendes, and A. N. Samukhin 353

Connectivity of growing random networks, P. L. Krapivsky, S. Redner, and F. Leyvraz 357

Competition and multiscaling in evolving networks, G. Bianconi and A.-L. Barabási 361

Universal behavior of load distribution in scale-free networks, K.-I. Goh, B. Kahng, and D. Kim 368

Spectra of "real-world" graphs: Beyond the semicircle law, I. J. Farkas, I. Derényi, A.-L. Barabási, and T. Vicsek 372

The degree sequence of a scale-free random graph process, B. Bol-lobás, O. Riordan, J. Spencer, and G. Tusnády 384

A model of large-scale proteome evolution, R.V. Solé, R. Pastor-Satorras, E. Smith, and T. B. Kepler 396

Modeling of protein interaction networks, A. Vázquez, A. Flammini, A. Maritan, and A. Vespignani 408

Chapter 5: Applications 415

5.1 Epidemics and rumors 415

5.2 Robustness of networks 424

5.3 Searching networks 428

Epidemics with two levels of mixing, F. Ball, D. Mollison, and G. Scalia-Tomba 436

The effects of local spatial structure on epidemiological invasions, M. J. Keeling 480

Small world effect in an epidemiological model, M. Kuperman and G. Abramson 489

Epidemic spreading in scale-free networks, R. Pastor-Satorras and A. Vespignani 493

A simple model of global cascades on random networks, D. J. Watts 497

Error and attack tolerance of complex networks, R. Albert, H. Jeong, and A.-L. Barabási 503

Resilience of the Internet to random breakdowns, R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin 507

Network robustness and fragility: Percolation on random graphs, D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts 510

Authoritative sources in a hyperlinked environment, J. M. Kleinberg 514

Search in power-law networks, L. A. Adamic, R. M. Lukose, A. R. Puniyani, and B. A. Huberman 543

Navigation in a small world, J. M. Kleinberg 551

Chapter 6: Outlook 553

References 559

Index 575