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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. Erd6s and A. R6nyi 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 Erdos, 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. BarabAsi 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. BarthB6lmy, 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. Barthel6my 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. Barabasi 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. BarabAsi 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. Derdnyi, A.-L. Barabdsi, and T. Vicsek 372 The degree sequence of a scale-free random graph process, B. Bol- lobAs, 0. Riordan, J. Spencer, and G. TusnBdy 384 A model of large-scale proteome evolution, R.V. Sol6, R. Pastor-Satorras, E. Smith, and T. B. Kepler 396 Modeling of protein interaction networks, A. V6zquez, 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. Barabdsi 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