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Emergence of Scaling in Random Networks
Abstract
Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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REFERENCES AND NOTES
1
Gallagher R., Appenzeller T., Science 284, 79 (1999);
; R. F. Service, ibid., p. 80.
2
G. Weng, U. S. Bhalla, R. Iyengar, ibid., p. 92.
3
C. Koch and G. Laurent, ibid., p. 96.
4
S. Wasserman and K. Faust, Social Network Analysis (Cambridge Univ. Press, Cambridge, 1994).
5
Members of the Clever project, Sci. Am.280, 54 (June 1999).
6
Albert R., Jeong H., Barabási A.-L., Nature 401, 130 (1999);
Barabási A.-L., Albert R., Jeong H., Physica A 272, 173 (1999);
; see also.
7
P. Erdős and
Rényi A., Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960);
; B. Bollobás, Random Graphs (Academic Press, London, 1985).
8
Lawrence S., Giles C. L., Science 280, 98 (1998);
; Nature 400, 107 (1999).
9
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 [
Huberman B. A., Adamic L. A., Nature 401, 131 (1999);
], the distribution of searches [
Huberman B. A., Pirolli P. L. T., Pitkow J. E., Lukose R. J., Science 280, 95 (1998);
], or the number of links per Web page (6).
10
Watts D. J., Strogatz S. H., Nature 393, 440 (1998).
11
Redner S., Eur. Phys. J. B 4, 131 (1998).
12
We also studied the neural network of the worm Caenorhabditis elegans (3, 10) and the benchmark diagram of a computer chip (see ). 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.
13
Milgram S., Psychol. Today 2, 60 (1967);
; M. Kochen, ed., The Small World (Ablex, Norwood, NJ, 1989).
14
J. Guare, Six Degrees of Separation: A Play (Vintage Books, New York, 1990).
15
Barthélémy M., Amaral L. A. N., Phys. Rev. Lett. 82, 15 (1999).
16
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).
17
Arthur W. B., Science 284, 107 (1999).
18
Preferential attachment was also used to model evolving networks (L. A. N. Amaral and M. Barthélémy, personal communication).
19
Banavar J. R., Maritan A., Rinaldo A., Nature 399, 130 (1999).
20
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.
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Published In
Science
Volume 286 | Issue 5439
15 October 1999
15 October 1999
Submission history
Received: 24 June 1999
Accepted: 2 September 1999
Published in print: 15 October 1999
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- Albert-László Barabási,
- Réka Albert
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