12-evolution_annot

12-evolution_annot -...

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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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ower w 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
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Preferential Attachment model power w In Preferential Attachment model power law degrees naturally emerge [Albert Barabasi ‘99] odes arrive in order 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 : ote: ref Attachment is not the only model to i d i j P ) ( Note: Pref. Attachment is not the only model to generate power law networks hat are other mechanisms giving power w 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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referential Preferential attachment: ower w 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
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referential attachment is a model of a Preferential attachment is a model of a growing network hat governs the network What governs the network growth and evolution? 1) Node arrival process: P1) Node arrival process: When nodes enter the network 2) Edge initiation process: P2) Edge initiation process: Each node decides when to initiate an edge 3) Edge destination process: 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] online social networks with 4 online social networks with exact edge arrival sequence r every edge ,v e know exact For every edge (u,v) we know exact time of the appearance t uv irectly observe mechanisms leading and so on for millions… Directly observe mechanisms leading to global network properties (F) (D) ) 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6 (A) (L)
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) (F) (D) Flickr: Exponential Delicious: Linear (A) (L) Answers: LinkedIn: Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu Sub linear Quadratic 10/27/2010 7
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ow long do nodes live? How long do nodes live? Node life time is the time between the 1 st and the st edge of a node last edge of a node ow often nodes “wake up” to create edges?
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This note was uploaded on 01/11/2011 for the course CS 224 at Stanford.

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12-evolution_annot -...

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