Complexity_ A Guided Tour - Melanie Mitchell [160]
“Although later studies debunked the theory”: See, e.g., Robbins, K. E., Lemey, P., Pybus, O. G., Jaffe, H. W., Youngpairoj, A. S., Brown, T. M., Salemi, M., Vandamme, A. M., and Kalish, M. L., U.S. human immunodeficiency virus type 1 epidemic: Date of origin, population history, and characterization of early strains. Journal of Virology, 77 (11), 2003, pp. 6359–6366.
“Recently, a group consisting of”: Liljeros, F., Edling, C. R., Nunes Amaral, L. A., Stanely, H. E., and Aberg, Y., The web of human sexual contacts. Nature, 441, 2001, pp. 907–908.
“similar results have been found in studies of other sexual networks”: e.g., Schneeberger, A., Mercer, C. H., Gregson, S. A., Ferguson, N. M., Nyamukapa, C. A., Anderson, R. M., Johnson, A. M., and Garnett, G. P., Scale-free networks and sexually transmitted diseases: A description of observed patterns of sexual contacts in Britain and Zimbabwe. Sexually Transmitted Diseases, 31 (6), 2004, pp. 380–387.
“A very clever yet simple method was proposed”: Cohen, R., ben-Avraham, D., and Havlin, S., Efficient immunization strategies for computer networks and populations. Physics Review Letters, 91 (24), 2003, p. 247901.
“one should target anti-virus methods”: Newman, M. E. J., Forrest, S., and Balthrop, J., Email networks and the spread of computer viruses. Physical Review E, 66, 2002, p. 035101.
“the ecology research community has recently seen a lot of debate”: See, e.g., Montoya, J. M. and Solé, R. V., Small world patterns in food webs. Journal of Theoretical Biology, 214 (3), 2002, pp. 405–412; Dunne, J. A., Williams, R. J., and Martinez, N. D., Food-web structure and network theory: The role of connectance and size. Proceedings of the National Academy of Science, USA, 99 (20), 2002, pp. 12917–12922; and Dunne, J. A., The network structure of food webs. In M. Pascual and J. A. Dunne (editors), Ecological Networks: Linking Structure to Dynamics in Food Webs. New York: Oxford University Press, 2006, pp. 27–86.
“Where Do Scale-Free Networks Come From?” Parts of this section were adapted from Mitchell, M., Complex systems: Network thinking. Artificial Intelligence, 170 (18), 2006, pp. 1194–1212.
“Albert-László Barabási and Réka Albert proposed”: Barabási, A.-L. and Albert, R., Emergence of scaling in random networks, Science, 286, 1999, pp. 509–512.
“this process and its power-law outcome had been discovered independently”: Yule, G. U., A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis. Philosophical Transactions of the Royal Society of London, Ser. B 213, 1924, pp. 21–87; Simon, H. A., On a class of skew distribution functions.” Biometrika 42 (3-4), 1955, p. 425; and Price, D. J., Networks of scientific papers. Science 149, 1965, pp. 510–515.
“the growth of so-called scientific citation networks”: e.g., see Redner, S., How popular is your paper? An empirical study of the citation distribution. European Physical Journal B, 4(2), 1998, pp. 131–134.
“what the writer Malcolm Gladwell called tipping points”: Gladwell, M., The Tipping Point: How Little Things Can Make a Big Difference. Boston: Little, Brown, 2000.
“A number of networks previously identified to be ‘scale-free’”: Clauset, A., Shalizi, C. R., and Newman, M. E. J., Power-law distributions in empirical data. Preprint, 2007, [http://arxiv.org/abs/0706.1062].
“Current assessments of the commonality of power-laws”: Keller, E. F., Revisiting ‘scale-free’ networks. BioEssays, 27, 2005, pp. 1060–1068.
“Our tendency to hallucinate”: Shalizi, C., Networks and Netwars, 2005. Essay at [http://www.cscs.umich.edu/~crshalizi/weblog/347.html].
“there turn out to be nine and sixty ways”: Shalizi, C., Power Law Distributions, 1/f noise, Long-Memory Time Series, 2007. Essay at [http://cscs.umich.edu/~crshalizi/notebooks/power-laws.html].