# Ger

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```					IEEE Intelligent Systems, Special Issue on Social Learning, 2010   1
Goal: analyzing how the networks evolve
over time
• Models of social networks
– networks follow power-law degree distribution,
– have a small diameter
– exhibit small-world structure and community structure
• Social networks is a function of time
– The Obama network
• Various Models have been studied
– many tools have been built (example)

2
Dynamic Models
• The preferential attachment model:
– assumes that new network nodes have a
higher probability of forming links with high-
degree nodes
– creating a “rich-get-richer” effect

Network diameter
shrinks over time
From: Leskovec et al. KDD’05
3
Questions raised in this paper
• Studying network formation strategies
– Microscopic level
• Graph Evolution Rules
– Association rules
– From current network configurations
• Predict future edges and nodes
• Rules
– Old-old
– Old-new
– New-new

4
Co-authorship Network
• http://www.arnetminer.org/viewperson.do?i
d=486660&name=Qiang%20Yang
sualExplorer#435931

5
Basic Concepts: Frequent Patterns
and Association Rules (from J. Han)

Transaction-id           Items bought      • Itemset X={x1, …, xk}
10                     A, B, C        • Find all the rules XY with min
20                      A, C            confidence and support
30                      A, D             – support, s, probability Pr(X,Y)
40                     B, E, F           – confidence, c, conditional
probability Pr(Y|X).
Customer        Customer
Let min_support = 50%,
min_conf = 50%:
A  C (50%, 66.7%)
C  A (50%, 100%)
Customer
6
Association Rules on Graphs
• First, we need to record
time stamps on graphs
– Nodes
– Edges
• A large-degree node (label 3),
which at time t is connected to
four medium-degree nodes
(label 2), at time t +1 will be
connected to a fifth node.
– The collaboration-rich
researcher gets richer.

7
G-span based GER Algorithm

8
Example GER Rules

9
Too many rules? Ranking

10
Datasets

11
Precision-Recall Curve

12
Dataset Statistics

13
14
15

```
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 views: 2 posted: 8/18/2011 language: English pages: 15