Upload
xanthus-clemons
View
37
Download
0
Embed Size (px)
DESCRIPTION
Jure Leskovec , CMU Lars Backstrom , Cornell Ravi Kumar, Yahoo! Research Andrew Tomkins, Yahoo! Research. Microscopic Evolution of Social Networks. Introduction. Social networks evolve with additions and deletions of nodes and edges - PowerPoint PPT Presentation
Citation preview
Microscopic Evolution of Social Networks
Jure Leskovec, CMULars Backstrom, CornellRavi Kumar, Yahoo! ResearchAndrew Tomkins, Yahoo! Research
Introduction
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)
We observe individual edge and node arrivals in large
social networks
Questions we ask
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?
The setting: Edge-by-edge evolution
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
Structure of our contributions
Experiments and the complete model of network evolution
Process Our finding
P1) Node arrivalP2) Edge initiationP3) Edge destination
Leskovec, Backstrom, Kumar & Tomkins: Microscopic Evolution of Social Networks, KDD '08
P1) How fast are nodes arriving?
(F) (D)
(A) (L)
Flickr: Exponential
Delicious: Linear
Answers: Sub-linear
LinkedIn:
Quadratic
Node lifetime is exponential
Lifetime a: time between node’s first and last edge
Node lifetime is exponential: p(a) = λ exp(-λa)
)()(),);(( dg eddp
2) How are edges initiated?
Edge gap δ(d): inter-arrival time between dth and d+1st edge
Degreed=1
d=3d=2
Edge time gap (time between 2 consecutive edges of a node)
Pro
bab
ilit
y
2) How do α & β evolve with degree?
Degree of Preferential Attachment
Edge Locality: closing triangles
Degree of PA & Edge locality
kkpe )(Networ
kτ
Gnm 0
PA 1F 1D 1A 0.9L 0.6
Network
% Δ
F 66%
D 28%
A 23%
L 50%
Fraction of triad closing
edges
How to close triangles?
We consider 25 strategies for choosing node v and then w
Compute likelihood of each strategy
Triad closing strategies
Log-likelihood improvement over the baseline
Strategy to select v (1st node)
Sele
ct
w (
2n
d n
od
e)
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
uw
v
The complete model
Process Our finding
P1) Node arrival
• Node arrival function is given• Node lifetime is exponential
P2) Edge initiation • Edge gaps:
P3) Edge destination
•1st edge is created preferentially• Use random-random to close triangles
dtettp )(
Analysis of our model
Theorem: node lifetimes and edge gaps lead to power law degree distribution
Interesting as temporal behavior predicts structural network property
Network
True γ
Predicted γ
F 1.73 1.74
D 2.38 2.30
A 1.90 1.75
L 2.11 2.08
Evolving the networks
Given our model one can take an existing network continue its evolution
Comparison with other models
Take Flickr at time T/2 and then further evolve it continue evolving it using PA and our model.
Summary and conclusion
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
Choosing edge source and destination