Albert-László Barabási

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The architecture of
complexity
Dana Farber Cancer Research Institute
Harvard University
and
Center for Complex Networks Research
University of Notre Dame
Complex systems
Business ties in US biotech-industry
Nodes: companies
investment
pharma
research labs
public
biotechnology
Links: collaborations
financial
R&D
http://ecclectic.ss.uci.edu/~drwhite/Movie
Erdös-Rényi model
(1960)
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Links: $%&
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collects all URL’s
found in a document and
follows them recursively
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Metabolic Network
Protein Interactions
Online communities
Nodes:
Links:
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Scale-free model
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Can Latecomers Make It? Fitness Model
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Bose-Einstein Condensation in Evolving Networks
Network
η
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Fit-gets-rich
Bose gas
− βε
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Bose-Einstein condensation
G. Bianconi and A.-L. Barabási, Physical Review Letters 2001; cond-mat/0011029
Spatial Distributions
%
Spatial Distribution of Routers
Fractal set
Box counting: N( ) ≡ No. of boxes
of size that contain routers
N( ) ~
=1.5
Preferential Attachment
• Compare maps taken at different times (∆
∆t = 6 months)
• Measure ∆ ( ), increase in No. of links for a node
with links
Preferential Attachment:
∆ ( )~
Modeling the effect of spatial distribution
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Robustness and fragility
node failure
Attacks
Failures
Albert, Jeong, Barabasi, Nature 406 378 (2000)
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Northeast Division
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Viral marketing
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http://www.orgnet.com
black: opinion leaders
red: influenced
green: uninfluenced
grey: undecided
500 randomly chosen clusters
Day 8
1
2
3
4
5
6
7
500 largest clusters
Day 8
1
2
3
4
5
6
7
Conclusions
WWW
Science collaboration
Language
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Citation pattern
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Zoltán N. Oltvai, U of Pittsburgh Med. School
Hawoong Jeong, KAIST, Corea
Réka Albert,
Penn State
Ginestra Bianconi, Trieste
Erzsébet Ravasz, Los Alamos
Stefan Wuchty, Northwestern U
Eivind Almaas,
Notre Dame
Livermore
Zoltan Dezso, Notre Dame
Gabor Szabo, Notre Dame
Alexei Vazquez, Notre Dame
Paris
Joao Oliveira, Notre Dame (Aveiro)
http://www.nd.edu/~networks
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