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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.