Navigating with Power Laws Aaron Clauset CAIDA / SFI Networks and - - PowerPoint PPT Presentation
Navigating with Power Laws Aaron Clauset CAIDA / SFI Networks and Navigability Working Group 8 August 2008 Milgram Study (1967) A question of social connectedness 60 letters sent to Wichita, Kansas Destination: wife of divinity stud.,
D.J. Watts and S.H. Strogatz, “Collective dynamics of small-world networks.” Nature 393 (1998) 440-442.
0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 1 80 90 100 110 120 130 140
powerlaw exponent, α mean routing time, T αopt~0.900 n~2*105 αopt~0.911 n~5*105 αopt~0.921 n~1*106 αopt~0.928 n~2*106
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link−length (log−binned), l frequency f(l) = O(l−0.7789) n≈103 f(l) = O(l−0.8239) n≈104 f(l) = O(l−0.8454) n≈105 f(l) = O(l−0.8760) n≈106
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25 50 75 100 125 150 network size, n mean routing time, T T(n) for α=d T(n) for αopt,αrewired T(n) =4.1log2(n)−7.39log(n) +6.08
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network size, n rewiring time, τ (trials per node) τ(n) data τ(n) =9+0.0304n0.77
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 initial exponent, α0 rewired exponent, αrewired τ=75 τ=150 τ=300 τ=500