Introduction to complex networks


    Alava, M. J. and Dorogovtsev, S. N. (2005), Complex networks created by aggregation, Phys. Rev. E 71, art. no. 036107.

    Albert, R., J., H., and Barabási, A.-L. (1999), Diameter of the World-Wide Web, Nature 401, pp. 130–131.

    Albert, R., Jeong, H., and Barabási, A.-L. (2000), Error and attack tolerance of complex networks, Nature 406, pp. 378–382.

    Amaral, L. and Ottino, J. (2004), Complex networks: Augmenting the framework for the study of complex systems, Eur. Phys. J. B 38, pp. 147–162.

    Amaral, L. A. N., Scala, A., Barthélémy, M., and Stanley, H. E. (2000), Classes of small-world networks, Proc. Natl. Acad. Sci. USA 97, pp. 11149–11152.

    Axelsen, J., Bernhardsson, S., Rosvall, M., Sneppen, K., and Trusina, A. (2006), Degree landscapes in scale-free networks, Phys. Rev. E 74, art. no. 036119.

    Ball, F., Mollison, D., and Scala-Tomba, G. (1997), Epidemics with two levels of mixing, Ann. Appl. Probab. 7, art. no. 1, pp. 46–89.

    Barabási, A.-L. (2001), The physics of the Web, PhysicsWorld .

    Barabási, A.-L. and Albert, R. (1999), Emergance of scaling in random networks, Science 286, pp. 509–512.

    Barabási, A.-L. and Albert, R. (2002), Statistical mechanics of complex networks, Rev. Mod. Phys. 74, pp. 47–98.

    Barabási, A.-L., Albert, R., and Jeong, H. (1999), Mean-feld theory for scale-free random networks, Physica A 272, pp. 173–187.

    Barabási, A.-L., Albert, R., Jeong, H., and Bianconi, G. (2000), Power-law distribution of the world wide web, Science 287, p. 2115.

    Barrat, A. and Weigt, M. (2000), On the properties of small-world network models, Eur. Phys. J. B 13, pp. 547–560.

    Boccaletti, S., V. Latora and, Y. M., Chavez, M., and Hwang, D.-U. (2006), Complex networks: Structure and dynamics, Phys. Rep. 424, pp. 175–308.

    Boguná, M. and Pastor-Satorras, R. (2002), Epidemic spreading in correlated complex networks, Phys. Rev. E 66, art. no. 047104.

    Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., and Wiener, J. (2000), Graph structure in the web, Comput. Netw. 33, pp. 309–320.

    Caldarelli, G., Capocci, A., de los Rios, P., and Munoz, M. A. (2002), Scale-free networks from varying vertex intrinsic fitness, Phys. Rev. Lett. 89, art. no. 258702.

    Carroll, L., Sylvie and Bruno Concluded (Macmillan and Co, London, 1893).

    Cohen-Cory, S. (2002), The developing synapse: Construction and modulation of synaptic structures and circuits, Science 298, pp. 770–776.

    Dennis, B. R. (1985), Solar hard X-ray bursts, Solar Phys. 100, pp. 465–490.

    Dorogovtsev, S. and Mendes, J. (2002), Evolution of networks, Adv. Phys. 51, pp. 1079–1187.

    Erdös, P. and Rényi, A. (1959), On random graphs I, Publ. Math. Debrecen 6, pp. 290–297.

    Faloutsos, M., Faloutsos, P., and Faloutsos, C., On power-law relationships of the Internet topology, in SIGCOMM (1999), pp. 251–262.

    Fell, D. A. and Wagner, A. (2000), The small world of metabolism, Nat. Biotechnol. 18, pp. 1121–1122.

    Field, G. B. and Saslow, W. C. (1965), A statistical model of the formation of stars and interstellar clouds, Astrophys. J. 142, p. 568.

    Freeman, L. C. (1977), A set of measures of centrality based on betweenness, Sociometry 40, pp. 35–41.

    Fry, D. B., Homo loquens: Man as a talking animal (Cambridge: CUP, 1977).

    Girvan, M. and Newman, M. E. J. (2002), Community structure in social and biological networks, Proc. Natl. Acad. Sci. 99, pp. 8271–8276.

    Goh, K.-I., Kahng, B., and Kim, D. (2001), Universal behavior of load distribution in scale-free networks, Phys. Rev. Lett. 87, art. no. 278701.

    Grönlund, A. and Holme, P. (2005), A network-based threshold model for the spreading of fads in society and markets, Adv. Complex Syst. 8, pp. 261–273.

    Grönlund, A. and Holme, P. (2004), Networking the seceder model: Group formation in social and economic systems, Phys. Rev. E 70, art. no. 036108.

    Grönlund, A., Sneppen, K., and Minnhagen, P. (2005), Correlations in networks associated to preferential growth, Phys. Scr. 71, pp. 680–682.

    Hughes, D. and Paczuski, M. (2003), Scale-free magnetic networks: Comparing observational data with a self-organizing model of the coronal field, Preprint astro-ph/0309230 .

    Hughes, D., Paczuski, M., Dendy, R. O., Helander, P., and McClements, K. G. (2003), Solar flares as cascades of reconnecting magnetic loops, Phys. Rev. Lett. 90, art. no. 131101.

    Ising, E. (1925), Beitrag zur Theorie des ferromagnetismus, Z. Physik 31, pp. 253–258.

    Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., and Barabási, A.-L. (2000), The large-scale organization of metabolic networks, Nature 407, pp. 651–654.

    Katz, L. and Powell, J. H. (1957), Probability distributions of random variables associated with a structure of the sample space of sociometric investigations, Ann. Math. Stat. 28, pp. 442–448.

    Kim, B. J., Trusina, A., Minnhagen, P., and Sneppen, K. (2005), Self-organized scale-free networks from merging and regeneration, Eur. Phys. J. B 43, pp. 669–672.

    Kleinberg, J., Small-world phenomena and the dynamics of information, in Proc. 32nd ACM Symposium on Theory of Computing (2000).

    Klemm, K. and Eguíluz, V. M. (2002), Growing scale-free networks with small-world behavior, Phys. Rev. E 65, art. no. 057102.

    Kochen, M., The small world (Ablex, Norwood, 1989).

    Krapivsky, P. L. (1993), Aggregation-annihilation processes with injection, Physica A 198, pp. 157–178.

    Krapivsky, P. L. and Redner, S. (2002), A statistical physics perspective on Web growth, Comput. Netw. 39, pp. 261–276.

    Krebs, V. E. (2002), Mapping networks of terrorist cells, Connections 24, art. no. 43–52.

    Latora, V. and Marchiori, M. (2001), Efficient behavior of small-world networks, Phys. Rev. Lett. 87, art. no. 198701.

    Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley, H. E., and Åberg, Y. (2001), The web of human sexual contacts, Nature 411, p. 907.

    Lin, R. P., Schwartz, R. A., Kane, S. R., Pelling, R. M., and Hurley, K. C. (1984), Solar hard X-ray microflares, Astrophys. J. 283, pp. 421–425.

    Lu, E. T. and Russell, R. J. (1991), Avalanches and the distribution of solar flares, Astrophys. J. 380, pp. 89–92.

    Maslov, S. and Sneppen, K. (2002), Specificity and stability in topology of protein networks, Science 296, art. no. 5569, pp. 910–913.

    Milgram, S. (1967), The small world problem, Psychol. Today 2, pp. 60–67.

    Minnhagen, P., Rosvall, M., Sneppen, K., and Trusina, A. (2004), Self-organization of structures and networks from merging and small-scale fluctuations, Physica A 340, pp. 725–732.

    Newman, M. E. J. (2002a), Assortative mixing in networks, Phys. Rev. Lett. 89, art. no. 208701.

    Newman, M. E. J. (2002b), The structure and function of networks, Comput. Phys. Commun. 147, pp. 40–45.

    Newman, M. E. J. (2003), Mixing patterns in networks, Phys. Rev. E 67, art. no. 026126.

    Newman, M. E. J. (2004a), Detecting community structure in networks, Eur. Phys. J. B 38, pp. 321–330.

    Newman, M. E. J. (2004b), Fast algorithm for detecting community structure in networks, Phys. Rev. E 69.

    Newman, M. E. J. (2006), Modularity and community structure in networks, Proc. Natl. Acad. Sci. USA 103, pp. 8577–8582.

    Newman, M. E. J., Barabási, A.-L., and Watts, D. J., The Structure and Dynamics of Networks (Princeton University Press, 2006).

    Newman, M. E. J. and Girvan, M. (2004), Finding and evaluating community structure in networks, Phys. Rev. E 69, art. no. 026113.

    Pastor-Satorras, R. and Vespignani, A. (2001), Epidemic spreading in scale-free networks, Phys. Rev. Lett. 86, pp. 3200–3203.

    Pastor-Satorras, R., Vázquez, A., and Vespignani, A. (2001), Dynamical and correlation properties of the Internet, Phys. Rev. Lett. 87, art. no. 258701.

    Popper, K. R., Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge and Kegan Paul, London, 1963).

    Price, D. J. (1965), Networks of scientific papers, Science 149, pp. 510–515.

    Price, D. J. (1976), A general theory of bibliometric and other cumulative advantage processes, J. Amer. Soc. Inform. Sci. 27, pp. 292–306.

    Rosvall, M., Trusina, A., Minnhagen, P., and Sneppen, K. (2005), Networks and cities: An information perspective, Phys. Rev. Lett. 94, art. no. 028701.

    Simon, H. A. (1955), On a class of skew distribution functions, Biometrika 42, pp. 425–440.

    Sneppen, K., Rosvall, M., Trusina, A., and Minnhagen, P. (2004), A simple model for self organization of bipartite networks, Europhys. Lett. 67, pp. 349–354.

    Snijders, T. A. B. (1991), Enumeration and simulation methods for 0-1 matrices with given marginal, Psychometrika 56, pp. 397–417.

    de Sola Pool, I. and Kochen, M. (1978), Contacts and influence, Soc. Netw. 1, pp. 1–48.

    Solomonoff, R. and Rapoport, A. (1951), Connectivity of random nets, B. Math. Biophys. 13, pp. 107–117.

    Takayasu, H. (1989), Steady-state distribution of generalized aggregation system with injection, Phys. Rev. Lett. 63, art. no. 2563.

    Trusina, A., Maslov, S., Minnhagen, P., and Sneppen, K. (2004), Hierarchy measures in complex networks, Phys. Rev. Lett. 92, art. no. 178702.

    Vázquez, A., Pastor-Satorras, R., and Vespignani, A. (2002), Large-scale topological and dynamical properties of the Internet, Phys. Rev. E 65, art. no. 066130.

    Waldrop, M. M., Complexity: The Emerging Science at the Edge of Order and Chaos (Simon and Schuster, New York, 1992).

    Watts, D. J., Six Degrees: The Science of a Connected Age (W. W. Norton and Co., New York, 2003).

    Watts, D. J. and Strogatz, S. H. (1998), Collective dynamics of ’small-world’ networks, Nature 393, pp. 440–442.

    West, G. B., Brown, J. H., and Enquist, B. J. (1997), A general model for the origin of allometric scaling laws in biology, Science 276, pp. 122–126.

    Wilson, E. O., Consilience: The Unity of Knowledge (Alfred A. Knopf, 1998).

    Zajdenweber, D. (1995), Business interruption insurance a risky business. A study on some paretian phenomena, Fractals 3, art. no. 3, pp. 95–110.

    Zipf, G., Human behavior and the principles of least effort (Addison Wesley, Cambridge, 1949).