11-power_laws_annot

11-power_laws_annot - CS224W:...

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CS224W: Social and Information Network Analysis re eskovec tanford University Jure Leskovec, Stanford University http://cs224w.stanford.edu
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10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
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loutsos loutsos d loutsos 999] [Faloutsos, Faloutsos and Faloutsos, 1999] ternet domain topology 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3 Internet domain topology
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arabasi lbert 1999] [Barabasi Albert, 1999] 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4 Power grid Web graph Actor collaborations
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roder Kumar aghoul aghavan [Broder, Kumar, Maghoul, Raghavan, Rajagopalan, Stata, Tomkins, Wiener, 2000] 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5
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[Leskovec et al. KDD ‘08] ke real network plot a histogram of Take real network plot a histogram of p k vs. k ickr cial Flickr social network n= 584,207, m=3,555,115 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6
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[Leskovec et al. KDD ‘08] lot the same data on g g is: Plot the same data on log log axis: Flickr social etwork network n= 584,207, m=3,555,115 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 7
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egrees are heavily skewed: Degrees are heavily skewed: Distribution P(X>x) is heavy tailed if: 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
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[Clauset Shalizi Newman 2007] ower w vs exponential on log g scales Power law vs. exponential on log log scales 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 9
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[Clauset Shalizi Newman 2007] arious names kinds and forms: Various names, kinds and forms: Long tail, Heavy tail, Zipf’s law, Pareto’s law (x) is proportional to: P(x) is proportional to: 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 10
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social systems ts of power ws: In social systems – lots of power laws: Pareto, 1897 –Wea lth distribution t k 926 i t i f i tt Lotka 1926 – Scientific output Yule 1920s – Biological taxa and subtaxa Zipf 1940s – Word frequency Simon 1950s –C ity populations 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 11
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[Clauset Shalizi Newman 2007] 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 12 Many other quantities follow heavy tailed distributions
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[Chris Anderson, Wired, 2004] 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 13
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CMU grad students at the G20 meeting in 10/25/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 14 Pittsburgh in Sept 2009
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Power law degree exponent is typically 2 < < 3 Web graph: in = 2.1, out = 2.4 [Broder et al. 00]
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11-power_laws_annot - CS224W:...

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