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Jure Leskovec, CMU Lars Backstrom, Cornell Ravi Kumar, Yahoo! Research Andrew Tomkins, Yahoo! Research.

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Presentation on theme: "Jure Leskovec, CMU Lars Backstrom, Cornell Ravi Kumar, Yahoo! Research Andrew Tomkins, Yahoo! Research."— Presentation transcript:

1 Jure Leskovec, CMU Lars Backstrom, Cornell Ravi Kumar, Yahoo! Research Andrew Tomkins, Yahoo! Research

2  Social networks evolve with additions and deletions of nodes and edges  We talk about the evolution but few have actually directly observed atomic events of network evolution (but only via snapshots) Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 This talk: We observed individual edge and node arrivals in large social networks and so on for millions…

3  Test individual edge attachment:  Directly observe mechanisms leading to global network properties ▪ E.g., What is really causing power-law degree distributions?  Compare models: via model likelihood  Compare network models by likelihood (and not by summary network statistics) ▪ E.g., Is Preferential Attachment best model? Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08

4  Three processes that govern the evolution  P1) Node arrival process: nodes enter the network  P2) Edge initiation process: each node decides when to initiate an edge  P3) Edge destination process: determines destination after a node decides to initiate Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 (F) (D) (A) (L)

5  Experiments and the complete model of network evolution ProcessOur finding P1) Node arrival P2) Edge initiation P3) Edge destination Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08

6 (F) (D) (A) (L) Flickr: Exponential Delicious: Linear Answers: Sub-linear LinkedIn: Quadratic Node arrival process is network dependent

7 Lifetime a: time between node’s first and last edge Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 Node lifetime is exponentially distributed: p(a) = λ exp(-λa) LinkedIn

8  What do we know so far? Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 ProcessOur finding P1) Node arrival Node arrival function is given Node lifetime is exponential P2) Edge initiation P3) Edge destination

9 Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 Edge gap δ(d): time between d th and d+1 st edge of a node Degree d=1 d=3 d=2 Edge time gap (time between 2 consecutive edges of a node) Probability Nodes of higher degree start adding edges faster and faster

10  What do we know so far? Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 ProcessOur finding P1) Node arrival Node arrival function is given Node lifetime is exponential P2) Edge initiation Edge gaps: P3) Edge destination

11 Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 G np PA (D) (F) (L) (A) Networkτ G np 0 PA1 F1 D1 A0.9 L0.6  We unroll the true network edge arrivals  Measure node degrees where edges attach First direct proof of preferential attachment!

12 u w v  Just before the edge (u,v) is placed how many hops is between u and v? Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 Network% Δ% Δ F66%66% D28% A23% L50% G np PA (D) (F) (L) (A) Fraction of triad closing edges Real edges are local. Most of them close triangles!

13  New triad-closing edge (u,w) appears next  We model this as: 1. Choose u’s neighbor v 2. Choose v’s neighbor w 3. Connect (u,w)  We consider 25 strategies for choosing v and then w  Can compute likelihood of each strategy  Under Random-Random: p(u,w) = 1/5*1/2+1/5*1 Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 u w v v’

14  Log-likelihood improvement over the baseline Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 Strategy to select v (1 st node) Select w (2 nd node) Strategies to pick a neighbor:  random: uniformly at random  deg: proportional to its degree  com: prop. to the number of common friends  last: prop. to time since last activity  comlast: prop. to com*last u w v random-random works well

15  The complete network evolution model Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 ProcessOur finding P1) Node arrival Node arrival function is given Node lifetime is exponential P2) Edge initiation Edge gaps: P3) Edge destination 1 st edge is created preferentially Use random-random to close triangles

16  Theorem: node lifetimes and edge gaps lead to power law degree distribution  Interesting as temporal behavior predicts structural network property Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 NetworkTrue γ Predicted γ F D A L Our theorem accurately predicts degree exponents γ as observed data

17  We observe network evolution at atomic scale  We use log-likelihood of edge placements to compare and infer models  Our findings  Preferential attachment holds but it is local  Triad closure is fundamental mechanism  We present a 3 process network evolution model  P1) Node lifetimes are exponential  P2) Edge interarrival time is power law with exp. cutoff  P3) Edge destination is chosen by random-random Gives more realistic evolution that other models Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08

18  More details and analyses in the paper  Thanks to Yahoo and LinkedIn for providing the data.  Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08

19 Edge gap δ(d): time between d th and d+1 st edge Edge interarrivals follow power law with exponential cutoff distribution: Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 How do α and β change with node degree?

20 Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08 This means nodes of higher degree start adding edges faster and faster Degree d=1 d=3 d=2


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