Reading Summaries

Mark Newman, Albert-László Barabási, and Duncan J. Watts: The Structure and Dynamics of Networks

F. Karinthy. 1929. "Chain-links," in Everything is Different.

Short story that appears to be the origin of the idea of "six degrees of separation."

Solomonoff, R. and A. Rapoport. 1951. Connectivity of random nets, Bulletin of Mathematical Biophysics, Volume 13, 1951.

Defines weak connectivity on a random net as the average number of reachable nodes as a function of net size and what we'd now call average degree or tie density. Their estimates suggest that even for low average connection density (e.g., 2) the overall connectedness of the net is close to it's asymptotic value. The implications are, for example, that even in the case of relatively low new infections per sick individual, epidemics can reach most of the population.

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 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. 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