1IEEE Intelligent Systems, Special Issue on Social Learning, 2010

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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)

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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

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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

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Co-authorship Network

• http://www.arnetminer.org/viewperson.do?id=486660&name=Qiang%20Yang

• http://academic.research.microsoft.com/VisualExplorer#435931

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

• Itemset X={x1, …, xk}

• Find all the rules XY with min confidence and support– support, s, probability Pr(X,Y)– confidence, c, conditional

probability Pr(Y|X).

Let min_support = 50%, min_conf = 50%:

A C (50%, 66.7%)C A (50%, 100%)

Customerbuys diaper

Customerbuys both

Customerbuys beer

Transaction-id Items bought

10 A, B, C

20 A, C

30 A, D

40 B, E, F

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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.

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G-span based GER Algorithm

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Example GER Rules

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Too many rules? Ranking

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Datasets

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Precision-Recall Curve

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Dataset Statistics

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