Epidemics and percolation in small-world networks

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 5, 2000, Pages 5678-5682

  Moore, Cristopher ^a,b   Newman, M E J ^a  

^a SANTA FE INSTITUTE   (Mexico)

^b University of NewMexico   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL NEURAL NETWORK; EPIDEMIOLOGY; HUMAN; STATISTICAL MODEL;

EPIDEMIOLOGIC METHODS; EPIDEMIOLOGY; HUMANS; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER);

PERCOLATION (SOLID STATE); PROBABILITY; SOLVENTS;

BOND PERCOLATION; DISEASE TRANSMISSION; EXACT SOLUTION; TRANSMISSION PROBABILITIES;

SMALL-WORLD NETWORKS;

EID: 0034186340     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.5678     Document Type: Article

References (12)

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2. D. J. Watts, Small Worlds (Princeton University Press, Princeton, NJ, 1999).
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6. D.J. Watts and S.H. Strogatz, Nature (London) 393, 440 (1998).
7. M.E.J. Newman and D.J. Watts, Phys. Rev. E 60, 7332 (1999).
8. C. Moukarzel, Phys. Rev. E (to be published).
9. M.E.J. Newman, C. Moore, and D.J. Watts, e-print cond-mat/9909165.
10. Technically this point is not a percolation transition, since it is not possible to create a system-spanning (i.e., percolating) cluster on a small-world graph. To be strictly correct, we should refer to the transition as “the point at which a giant component first forms.” This is something of a mouthful, however, so we will bend the rules a little and continue to talk about “percolation” in this paper.
11. G. T. Barkema and M. E. J. Newman, in Monte Carlo Methods in Chemical Physics, edited by D. Ferguson, J. I. Siepmann, and D. G. Truhlar (Wiley, New York, 1999).
12. We have also experimented with finite-size scaling as a method for calculating (Formula presented) Such calculations are, however, prone to inaccuracy because, as pointed out in Ref. 7, the correlation length scaling exponent (Formula presented), which governs the behavior of (Formula presented) as system size is varied, depends on the effective dimension of the graph, which itself changes with system size. Thus the exponent can at best be considered only approximately constant in a finite-size scaling calculation. Rather than introduce unknown errors into the value of (Formula presented) as a result of this approximation, we have opted in the present work to quote direct measurements of (Formula presented) on large systems as our best estimate of the percolation threshold.