Searching in small-world networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 3 2, 2003, Pages 361061-361065

  De Moura, Alessandro P S ^a   Motter, Adilson E ^b   Grebogi, Celso ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; NETWORK PROTOCOLS; NEURAL NETWORKS; RANDOM PROCESSES; ROUTERS; TELECOMMUNICATION LINKS;

SMALL-WORLD NETWORKS;

INTERNET;

EID: 0242411892     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. B. Bollobás, Modern Graph Theory (Springer-Verlag, New York, 1991).
2. D.J. Watts, Small Worlds (Princeton University Press, Princeton, NJ, 1999).
3. D.J. Watts and S.H. Strogatz, Nature (London) 393, 440 (1998).
4. S. Milgram, Psychol. Today 1, 61 (1967).
5. D.J. Watts, P.S. Dodds, and M.E.J. Newman, Science 296, 1302 (2002).
6. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 401, 130 (1999).
7. A.E. Motter, A.P.S. de Moura, Y.-C. Lai, and P. Dasgupta, Phys. Rev. E 65, 065102 (2002).
8. S.H. Strogatz, Nature (London) 410, 268 (2001).
9. R. Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002).
10. B.J. Kim, C.N. Yoon, S.K. Han, and H. Jeong, Phys. Rev. E 65, 027103 (2002); L.A. Adamic, R.M. Lukose, A.R. Puniyani, and B.A. Huberman, ibid. 64, 046135 (2001).
11. B.J. Kim, C.N. Yoon, S.K. Han, and H. Jeong, Phys. Rev. E 65, 027103 (2002); L.A. Adamic, R.M. Lukose, A.R. Puniyani, and B.A. Huberman, ibid. 64, 046135 (2001).
12. J.M. Kleinberg, Nature (London) 406, 845 (2000).
13. R. Guimerà, A. Días-Guilera, F. Vega-Redondo, A. Cabrales, and A. Arenas, Phys. Rev. Lett. 89, 248701 (2002).
14. F. Menczer, Proc. Natl. Acad. Sci. U.S.A. 99, 14014 (2002).
15. D.R. White and M. Houseman, Complexity 8, 72 (2003).
16. i+1 forever. To prevent this, we establish that if the same link in the network is about to be crossed twice, the next node is chosen randomly in the network, and then it proceeds as before.
17. The average number of links in the nodes visited by the searching process is actually slightly larger than 2k, because nodes with larger number of links are more likely to be visited. We have neglected this difference, which is very small in the case of the Watts-Strogatz network.
18. T. Nishikawa, A. E. Motter, Y.-C. Lai, and F. C. Hoppensteadt, Phys. Rev. Lett. 91, 014101 (2003).