Emergence of scaling in random networks

Science

Volumn 286, Issue 5439, 1999, Pages 509-512

  Barabási, Albert László ^a   Albert, Réka ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; RANDOMIZATION;

EID: 0038483826     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.286.5439.509     Document Type: Article

References (26)

1. R. Galtagher and T. Appenzeller, Science 284, 79 (1999); R. F. Service, ibid., p. 80.
2. R. Galtagher and T. Appenzeller, Science 284, 79 (1999); R. F. Service, ibid., p. 80.
3. C. Weng, U. S. Bhalla, R. Iyengar, ibid., p. 92.
4. C. Koch and G. Laurent, ibid., p. 95.
5. S. Wasserman and K. Faust, Social Network Analysis (Cambridge Univ. Press, Cambridge, 1994).
6. Members of the Clever project, Sci. Am. 280, 54 (June 1999).
7. R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999); A.-L. Barabási, R. Albert, H. Jeong, Physica A 272, 173 (1999); see also http://www.nd.edu/-net-works.
8. R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999); A.-L. Barabási, R. Albert, H. Jeong, Physica A 272, 173 (1999); see also http://www.nd.edu/-net-works.
9. P. Erdös and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960); B. Bollobás, Random Graphs (Academic Press, London, 1985).
10. P. Erdös and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960); B. Bollobás, Random Graphs (Academic Press, London, 1985).
11. S. Lawrence and C. L. Giles, Science 280, 98 (1998); Nature 400, 107 (1999).
12. S. Lawrence and C. L. Giles, Science 280, 98 (1998); Nature 400, 107 (1999).
13. In addition to the distribution of incoming links, the WWW displays a number of other scale-free features characterizing the organization of the Web pages within a domain [B. A. Huberman and L. A. Adamic, Nature 401, 131 (1999)], the distribution of searches [B. A. Huberman, P. L. T. Pirolli, J. E. Pitkow, R. J. Lukose, Science 280, 95 (1998)], or the number of links per Web page (6).
14. In addition to the distribution of incoming links, the WWW displays a number of other scale-free features characterizing the organization of the Web pages within a domain [B. A. Huberman and L. A. Adamic, Nature 401, 131 (1999)], the distribution of searches [B. A. Huberman, P. L. T. Pirolli, J. E. Pitkow, R. J. Lukose, Science 280, 95 (1998)], or the number of links per Web page (6).
15. D. J. Watts and S. H. Strogatz, Nature 393, 440 (1998).
16. S. Redner, Eur. Phys. J. B 4, 131 (1998).
17. We also studied the neural network of the worm Caenorhabditis elegans (3, 10) and the benchmark diagram of a computer chip (see http://vlsicad.cs. ucla.edu/~cheese/ispd98.html). We found that P(k) for both was consistent with power-Law tails, despite the fact that for C. elegans the relatively small size of the system (306 vertices) severely limits the data quality, whereas for the wiring diagram of the chips, vertices with over 200 edges have been eliminated from the database.
18. S. Milgram, Psychol. Today 2, 60 (1967); M. Kochen, ed., The Small World (Ablex, Norwood, NJ, 1989).
19. S. Milgram, Psychol. Today 2, 60 (1967); M. Kochen, ed., The Small World (Ablex, Norwood, NJ, 1989).
20. J. Guare, Six Degrees of Separation: A Play (Vintage Books, New York, 1990).
21. M. Barthélémy and L. A. N. Amaral, Phys. Rev. Lett. 82, 15 (1999).
22. For most networks, the connectivity m of the newly added vertices is not constant. However, choosing m randomly will not change the exponent γ (Y. Tu, personal communication).
23. W. B. Arthur, Science 284, 107 (1999).
24. Preferential attachment was also used to model evolving networks (L. A. N. Amaral and M. Barthélémy, personal communication).
25. J. R. Banavar, A. Maritan, A. Rinaldo, Nature 399, 130 (1999).
26. We thank D. J. Watts for providing the C. elegans and power grid data, B. C. Tjaden for supplying the actor data, H. Jeong for collecting the data on the WWW, and L. A. N. Amaral for helpful discussions. This work was partially supported by NSF Career Award DMR-9710998.