Albert-László Barabási - 公益財団法人 NEC C&C財団 · The Architecture of Complexity:...
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The Architecture of Complexity:From the Topology of the WWW to the
Structure of the Cell
AlbertAlbert--LLáászlszlóó BarabBarabáásisiCenter for Complex Networks ResearchCenter for Complex Networks Research
Northeastern UniversityNortheastern University
Department of Medicine and CCSBDepartment of Medicine and CCSB
Harvard Medical School Harvard Medical School
www.BarabasiLab.com
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Internet
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Red, blue, or green: departments Yellow: consultants
Grey: external experts
Structure of an organization
www.orgnet.com
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Business ties in US biotech-industry
Nodes: companiesinvestmentpharmaresearch labspublicbiotechnology
Links: collaborationsfinancialR&D http://ecclectic.ss.uci.edu/~drwhite/Movie
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Complex systems
Made of many non-identical elementsconnected by diverse interactions.
NETWORK
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Erdös-Rényi model(1960)
- Democratic
- Random
PPááll ErdErdööss(1913-1996)
Connect with probability p
p=1/6N=10
⟨k⟩ ~ 1.5 Poisson distribution
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World Wide Web
Over 10 billion documents
ROBOT: collects all URL’s found in a document and follows them recursively
Nodes: WWW documents Links: URL links
R. Albert, H. Jeong, A-L Barabási, Nature, 401 130 (1999).
Expected
P(k) ~ k-γ
FoundSc
ale-
free
Net
wor
kEx
pone
ntia
l Net
wor
k
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INTERNET BACKBONE
(Faloutsos, Faloutsos and Faloutsos, 1999)
Nodes: computers, routers Links: physical lines
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Nodes: online user Links: email contact
Ebel, Mielsch, Bornholdtz, PRE 2002.
Online communities
Kiel University log files 112 days, N=59,912 nodes
Pussokram.com online community; 512 days, 25,000 users.
Holme, Edling, Liljeros, 2002.
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Nodes: scientist (authors)
Links: write paper together
SCIENCE COAUTHORSHIP
(Newman, 2000, Barabási et al 2001)
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SCIENCE CITATION INDEX
(γ = 3)
Nodes: papers Links: citations
(S. Redner, 1998)
P(k) ~k-γ
648
25
H.E. Stanley,...
1736 PRL papers (1988)
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Swedish sex-webNodes: people (Females; Males)Links: sexual relationships
Liljeros et al. Nature 2001
4781 Swedes; 18-74; 59% response rate.
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Origin of SF networks: Growth and preferential attachment
Barabási & Albert, Science 286, 509 (1999)
jj
ii k
kkΣ
=Π )(
P(k) ~k-3
(1) Networks continuously expand by the addition of new nodesWWW : addition of new documents
GROWTH:add a new node with m links
PREFERENTIAL ATTACHMENT: the probability that a node connects to a node with k links is proportional to k.
(2) New nodes prefer to link to highly connected nodes.WWW : linking to well known sites
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SF model: k(t)~t ½ (first mover advantage)
Fitness model: fitness (η ) k(η,t)~tβ(η)
β(η) =η/C
Π(ki) ≅ηi ki
ηj k jj∑
Fitness Model: Can Latecomers Make It?
time
Deg
ree
(k)
Bianconi & Barabási, Physical Review Letters 2001; Europhys. Lett. 2001.
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protein-gene interactions
protein-protein interactions
PROTEOME
GENOME
Citrate Cycle
METABOLISM
Bio-chemical reactions
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Metabolic Network Protein Interactions
Jeong, Tombor, Albert, Oltvai, & Barabási, Nature (2000); Jeong, Mason, Barabási &. Oltvai, Nature (2001); Wagner & Fell, Proc. R. Soc. B (2001)
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Human Interaction Network
Rual et al. Nature 2005; Stelze et al. Cell 2005
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RobustnessComplex systems maintain their basic functions even under errors and failures
(cell → mutations; Internet → router breakdowns)
node failure
fc
0 1Fraction of removed nodes, f
1
S
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Robustness of scale-free networks
1
S
0 1ffc
Attacks
γ ≤ 3 : fc=1(R. Cohen et al PRL, 2000)
Failures
Albert, Jeong, Barabási, Nature 406 378 (2000)
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Achilles’ Heel of complex networks
Internet
failureattack
R. Albert, H. Jeong, A.L. Barabási, Nature 406 378 (2000)
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Hubs and Essentiality
Jeong, Mason, Barabási, and Oltvai, Nature 411, 41-42 (2001
18% 24% 62%
Hubs evolve slower: they are more alike in different organisms[H Fraser et al., Science (2002). Krylov, et al. Genome Res.(2003)]
Hub removal has more phenotypic consequences [Yu et al. Science (2008)]
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ρ
λλ c
Active phaseVirus death
Pastor Satorras & Vespignani, Physical Review Letters (2001)
Biology:If a virus is not too infectious, it will die out
Economics and social sciences:If a product or an idea is not too ‘sticky,’ it will not succeed.
λ: spreading rate of a virusρ: density of infected users
λ c= <k2><k> λ c→ 0<k2> ∞
Epidemic threshold in scaleEpidemic threshold in scale--free networksfree networks
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NRC Panel on “Network Science”
What is “network science”?An attempt to understand networks emerging in nature, technology and society
using a unified set of tools and principles.
What is new here?Despite the apparent differences, many networks emerge and evolve driven by a
fundamental set of laws and mechanism.
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www.BarabasiLab.com
RRéékaka Albert, Albert, Penn StatePenn State
HawoongHawoong JeongJeong, , KAIST, KoreaKAIST, Korea
GinestraGinestra BianconiBianconi, , ICTP, TriesteICTP, Trieste
KwangKwang--Il Il GohGoh, , Korea UniversityKorea University
Cesar Hidalgo, Cesar Hidalgo, Notre DameNotre Dame
Mark Vidal, Mark Vidal, DanaDana--Farber, HarvardFarber, Harvard
Michael E. Michael E. CusickCusick, , Dana Farber, HarvardDana Farber, Harvard
David Valle, David Valle, Johns HopkinsJohns Hopkins
Barton Childs, Barton Childs, Johns HopkinsJohns Hopkins
Nicholas Christakis, Nicholas Christakis, HarvardHarvard
DeokDeok--Sun Lee, Sun Lee, Northeastern University & DFNortheastern University & DF
JuyongJuyong Park, Park, Northeastern University & DFNortheastern University & DF
ZoltanZoltan N. N. OltvaiOltvai, , PitssburghPitssburgh Medical SchoolMedical School
DashunDashun Wang, Wang, Northeastern UniversityNortheastern University