Small-world networks: Evidence for a crossover picture

Physical Review Letters

Volumn 82, Issue 15, 1999, Pages 3180-3183

  Barthélémy, Marc ^a,b   Nunes Amaral, Luís A ^a  

^a Boston University ^*  (United States)

^b CEA BIII   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038740915     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.82.3180     Document Type: Article

References (33)

1. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971).
2. Correlations and Connectivity: Geometry Aspects of Physics, Chemistry and Biology, H. E. Stanley and N. Ostrowsky (Kluwer Academic Publishers, Dordrecht, 1990).
3. Fractals and Disordered Systems, A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1996), 2nd ed.
4. A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 1980).
5. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
6. M. Gerhardt, H. Schuster, and J. J. Tyson, Science. 247, 1563 (1990).
7. M. A. Nowak and R. M. May, Nature (London). 359, 826 (1992).
8. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, England, 1994).
9. Y. Braiman, J. F. Lindner, and W. L. Ditto, Nature (London). 378, 465 (1995).
10. J. J. Collins, C. C. Chow, and T. T. Imhoff, Nature (London). 376, 236 (1995).
11. J. J. Hopfield and A. V. M. Hertz, Proc. Natl. Acad. Sci U.S.A. 92, 6655 (1995).
12. J. P. Crutchfield and M. Mitchell, Proc. Natl. Acad. Sci. U.S.A. 92, 10 742 (1995).
13. K. Wiesenfeld, Physica (Amsterdam). 222B, 315 (1996).
14. G. Hess, Ecology. 77, 1617 (1996).
15. M. Kretschmar and M. Morris, Math. Biosci. 133, 165 (1996).
16. P. C. Bressloff, S. Comber, and B. De Souza, Phys. Rev. Lett. 79, 2791 (1997).
17. B. Bollobás, Random Graphs (Academic Press, London, 1985).
18. P. Erdös and A. Rényi, Publ. Math. Debrecen. 6, 290 (1959);
19. P. Erdös, A. Rényi, Publ. Math. Inst. Hungar. Acad. Sci. 5, 17 (1960);
20. P. Erdös, A. Rényi, Bull. Inst. Int. Statis. Tokyo. 38, 343 (1961).
21. K. Christensen, R. Donangelo, B. Koiller, and K. Sneppen, Phys. Rev. Lett. 81, 2380 (1998).
22. A. Barrat and R. Zecchina, Phys. Rev. B. 59, R1299 (1999); cond-mat/9811033.
23. B. Luque and R. V. Solé, Phys. Rev. E. 55, 257 (1997).
24. D. Cassi, Phys. Rev. Lett. 76, 2941 (1996).
25. T. Kottos and U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997).
26. R. Axelrod, The Evolution of Cooperation (Basic Books, New York, 1984).
27. S. Jain and S. Krishna, Phys. Rev. Lett. 81, 5684 (1998);
28. D. J. Watts and S. H. Strogatz, Nature (London). 393, 440 (1998).
29. J. J. Collins and C. C. Chow, Nature (London). 393, 409 (1998).
30. S. Milgram, Psychology Today. 2, 60 (1967).
31. The Small World, M. Kochen (Ablex, Norwood, NJ, 1989).
32. H. Herzel, Fractals. 6, 301 (1998).
33. M. Gondran and M. Minoux, Graphs and Algorithms (Wiley, New York, 1984). See page 48 for details of the Moore-Dijkstra algorithm.