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12-evolution_annot

# 12-evolution_annot - CS224W:...

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CS224W: Social and Information Network Analysis Jure Leskovec Stanford University Jure Leskovec, http://cs224w.stanford.edu

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Power law degree Power law degree distributions How do power law degree networks look like? Function is scale free if: f(ax) = c f(x) 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2 Random network (Erdos Renyi random graph) Scale free (power law) network
In Preferential Attachment model power law In Preferential Attachment model power law degrees naturally emerge [Albert Barabasi ‘99] Nodes arrive in order A new node j creates m out links Prob. of linking to a node i is proportional to its degree d i : Note: Pref Attachment is not the only model to i d i j P ) ( Pref. Attachment is not the only model to generate power law networks What are other mechanisms giving power law degree networks? 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3

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Preferential attachment: Power law Power law degree distributions Node degrees: But no local clustering Can we get multiple Clustering coefficient: properties? 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4
Preferential attachment is a model of a growing network What governs the network growth and evolution? P1) Node arrival process: When nodes enter the network P2) Edge initiation process: Each node decides when to initiate an edge P3) Edge destination process: The node determines destination of the edge 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5

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[Leskovec et al. KDD 08] 4 online social networks with exact edge arrival sequence For every edge (u,v) we know exact time of the appearance t uv Directly observe mechanisms leading and so on for millions… to global network properties (F) (D) (A) 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6 (L)
(F) (D) (D) Flickr: Exponential Delicious: Linear (A) (L) Answers: S b li LinkedIn: Q d ti Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu Sub linear Quadratic 10/27/2010 7

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How long do nodes live? Node life time is the time between the 1 st and the last edge of a node How often nodes “wake up” to create edges? How often nodes wake up to create edges? 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
Lifetime a Li k dI : time between node’s first d l t d LinkedIn and last edge Node lifetime is exponential : p(a) = λ exp( ‐λ a) 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 9

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How often nodes “wake up” to create edges? How often nodes wake up to create edges?
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