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Densification Power Law [Leskovec et al. KDD 05] the number of edges grows faster than the number of nodes – average g degree g is increasing g or equivalently a … densification exponent: 1 ≤ a ≤ 2: a=1: linear growth – constant out‐degree (traditionally assumed) a=2: quadratic growth – clique 10/15/2009 Jure Leskovec, <strong>Stanford</strong> CS322: Network Analysis
Prior work on Power Law graphs hints at Slowly growing diameter: diameter ~ O(log N) diameter ~ O(log log N) Wh What is i happening h i in i real l data? d ? 10/15/2009 Jure Leskovec, <strong>Stanford</strong> CS322: Network Analysis [Leskovec et al. KDD 05]
Page 1 and 2: CS 322: (Social and Information) Ne
Page 3 and 4: What is the relation between the nu
Page 5: Citations among physics papers 199
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 and 32: Claim: If F t is taken from a logno
Page 33 and 34: Consider continuous version of logn
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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