12-evolution_annot

# Edge gap δ d time between d th and d1 st edge of a

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Edge gap δ (d) : time between d th and d+1 st edge of a node: Let t i (d) be the creation time of d th edge of node i δ i (d) = t i (d+1) t i (d) Then δ (d) is a distribution (histogram) of δ i (d) over all nodes i 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 10

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Edge gap δ (d) : Edge gap δ (d) : inter arrival time between LinkedIn d th and d+1 st edge For every d we get a differentplot e p g ) , ; ( 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 11
As the degree of the node degree increases As the degree of the node degree increases, how α and β change? 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 12

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α is const, β linear in d – gaps get smaller with d linear in d gaps get smaller with d d g e d p ) , , ; ( ty Probabilit Degree d=1 d=3 d=2 P 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, Edge gap 13
Source node i wakes up and creates an edge Source node i wakes up and creates an edge How does i select a target node j ? What is the degree of the target j ? Do preferential attachment really hold? How many hops away if the target j ? Are edges attaching locally? 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 14

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[w/ Backstrom Kumar Tomkins, KDD ’08] Are edges more likel to connect to higher Are edges more likely to connect to higher degree nodes? k k ) ( p e G np PA Network τ G Flickr np 0 PA 1 Flickr 1 Delicious 1 Answers 0.9 LinkedIn 0.6 15 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis,
[w/ Backstrom Kumar Tomkins, KDD ’08] Just before the edge (u w) is placed how many (u,w) hops is between u and w ? Fraction of triad closing edges Network % Δ Flickr 66% G np PA Delicious 28% Answers 23% k d Fli k w LinkedIn 50% Real edges are local Flickr u v Real edges are local. Most of them close triangles! 16 10/27/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis,

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New triad closing edge (u w) appears next New triad closing edge (u,w) We model this as: 1 Ch i hb w v’ 1. Choose u ’s neighbor v 2. Choose v ’s neighbor w ( ) u v 3. Connect (u,w) Compute edge prob. under Random R d ( ) Random: p(u,w) = “S f h ( ) “Score” of a graph = p(u,w) Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 10/27/2010 17
Impro ement o er the baseline Improvement over the baseline: Strategy to select v (1 st node) ode) t w (2 nd no Select Strategies to pick a neighbor: random : uniformly at random deg : proportional to its degree com : prop. to the number of common friends u w v Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, last : prop. to time since last activity comlast : prop. to com * last 10/27/2010 18

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• Fall '09
• Graph Theory, Jure Leskovec, Information Network Analysis, Stanford CS224W

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