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If there exists a lower bound: X t max( , F t t 1 1X t t 1 1) [Mitzenmacher] then Xt converges to a power law distribution [Champernowne [Champernowne, 1953] Lognormal model easily pushed to a power law model 10/15/2009 Jure Leskovec, <strong>Stanford</strong> CS322: Network Analysis
Consider continuous version of lognormal generative model: At time t, log X t is normal with mean t t and variance 2 t Suppose observation time is distributed exponentially E.g., When Web size doubles every year. RResulting lti distribution di t ib ti is i Double D bl Pareto. P t [Mitzenmacher] Between lognormal and Pareto. Li Linear tail tilon a log‐log l l chart, h t but b ta lognormal l lb body. d 10/15/2009 Jure Leskovec, <strong>Stanford</strong> CS322: Network Analysis
Page 1 and 2: CS 322: (Social and Information) Ne
Page 3 and 4: What is the relation between the nu
Page 5 and 6: Citations among physics papers 199
Page 7 and 8: Prior work on Power Law graphs hint
Page 9 and 10: Is shrinking diameter just j a cons
Page 11 and 12: [Leskovec et al. TKDD 07] How does
Page 13 and 14: [Leskovec et al. TKDD 07] Densific
Page 15 and 16: Let Let’s s assume the community
Page 17 and 18: n=2k n = 2 nodes reside in the lea
Page 19 and 20: What is expected out‐degree out d
Page 21 and 22: Claim: The Community Guided Attachm
Page 23 and 24: [Leskovec et al. TKDD 07] Communit
Page 25 and 26: Expected degree of a node at height
Page 27 and 28: f ( x) Properties: 1 2 2 1 x e (
Page 29 and 30: Question: Is this distribution logn
Page 31: Claim: If F t is taken from a logno
Page 35 and 36: Hierarchical model that produces po
Page 37 and 38: Mandelbrot experiment: design a lan
Page 39 and 40: Each j letter word has frequency (c

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