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The structure and function of networks. (English) Zbl 1001.68931
Summary: Many systems take the form of networks, including the Internet, distribution and transport networks, neural networks, food webs, and social networks. The characterization and modeling of these systems has proved amenable to treatment using techniques drawn from statistical and computational physics, and has as a result attracted considerable attention in the physics literature in recent years. In this paper the author reviews some of the interesting issues in this area and recounts some recent work on these issues by himself and by others.

MSC:
68U99 Computing methodologies and applications
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[1] Strogatz, S.H., Nature, 410, 268-276, (2001)
[2] Albert, R.; Barabási, A.-L., Rev. mod. phys., 74, 47-97, (2002)
[3] Pool, I.; Kochen, M., Social networks, 1, 1-48, (1978)
[4] Milgram, S., Psychol. today, 2, 60-67, (1967)
[5] Newman, M.E.J.; Strogatz, S.H.; Watts, D.J., Phys. rev. E, 64, 026118, (2001)
[6] Watts, D.J.; Strogatz, S.H., Nature, 393, 440-442, (1998)
[7] Erdős, P.; Rényi, A., Publ. math., 6, 290-297, (1959)
[8] Molloy, M.; Reed, B., Random struct. algorithms, Combin. probab. comput., 7, 295-305, (1998)
[9] Newman, M.E.J., Phys. rev. E, 64, 016131-016132, (2001)
[10] Barabási, A.-L.; Albert, R., Science, 286, 509-512, (1999)
[11] Newman, M.E.J., Phys. rev. E, 64, 025102, (2001)
[12] Jeong, H.; Neda, Z.; Barabási, A.-L.
[13] Newman, M.E.J., J. stat. phys., 101, 819-841, (2000)
[14] Warren, C.P.; Sander, L.M.; Sokolov, I.M.
[15] Watts, D.J., Small worlds, (1999), Princeton University Press Princeton · Zbl 0940.82029
[16] Jin, E.M.; Girvan, M.; Newman, M.E.J., Phys. rev. E, 64, 046132, (2001)
[17] Davidsen, J.; Ebel, H.; Bornholdt, S.
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