The Architecture of Complexity:From Networks to Economic Systems
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
Internet
Red, blue, or green: departments Yellow: consultants
Grey: external experts
Structure of an organization
www.orgnet.com
Business ties in US biotech-industry
Nodes: companiesinvestmentpharmaresearch labspublicbiotechnology
Links: collaborationsfinancialR&D http://ecclectic.ss.uci.edu/~drwhite/Movie
World trade imbalance web for 2000. Directed network of merchandise trade imbalances between world countries. Each country appears as a node and the
direction of the arrow follows that of the net flow of money. (Serrano et al 2007).
Trade Imbalance Network
Japanese Credit Network Between Banks
An Analysis of the Japanese Credit Network
G. De Masi, Y. Fujiwara, M. Gallegati, B. Greenwald, J. E. Stiglitz (16 Jan 2009)
Erdös-Rényi model(1960)
- Democratic
- Random
PPáál Erdl Erdööss(1913-1996)
Connect with probability p
p=1/6N=10
⟨k⟩ ~ 1.5 Poisson distribution
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
INTERNET BACKBONE
(Faloutsos, Faloutsos and Faloutsos, 1999)
Nodes: computers, routers Links: physical lines
Origin of SF networks: Growth and preferential attachment
Barabási & Albert, Science 286, 509 (1999)
jj
ii k
kkΣ
=Π )(
P(k) ~k-3
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
(1) Networks continuously expand by the addition of new nodesWWW : addition of new documents
GROWTH:add a new node with m links
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.
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
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)
B. Balassa, The Review of Economics and Statistics 68, 315 (1986).B. Balassa, The Review of Economics and Statistics 68, 315 (1986).
Denotes where region has RCA
KEY
Japan 1985 Japan 2000
http://www.nd.edu/~networks/productspace/index.htm
Iterated Diffusion (φ=0.55)
0.5 1 1.5 2 2.5
x 104
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2x 104
ALB
ARG
ARMAUS
AUT
BDI
BENBFA
BGD
BGR
BHRBHS
BLRBLZ
BOLBRA
BRBCAF
CANCHL
CHN
CIV
CMR
COLCRI
CZEDEUDNK
DOM
DZA
ECUEGY
ESPEST
ETH
FIN
FJI
GAB
GBR
GEO
GHA
GIN
GMB
GRCGTMGUY
HKG
HND
HRV
HTIHUNIDNIND
IRLIRN ISL
ISR
ITA
JAM JOR
JPN
KAZKENKGZ KNAKOR
LBNLKA LTULVAMAC
MARMDAMDG
MEX
MLIMLTMNG MOZMUS
MWIMYS
NCL
NER
NGA
NIC
NLDNORNPLNZL
OMNPAKPAN
PERPHL
PNG
POLPRT
PRYROMRUS
RWA
SAU
SDNSEN SGPSLE
SLV
SVKSVNSWE
SYR
TGO
THA
TJKTKMTTO
TUR
TZAUGA
UKRURY
USA
VEN
WSM
ZAF
ZMB
ZWE
1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
2.5x 104
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.
www.BarabasiLab.com
RRééka Albert, ka Albert, Penn StatePenn State
Hawoong Jeong, Hawoong Jeong, KAIST, KoreaKAIST, Korea
Ginestra Bianconi, Ginestra Bianconi, ICTP, TriesteICTP, Trieste
KwangKwang--Il Goh, Il Goh, Korea UniversityKorea University
Cesar Hidalgo, Cesar Hidalgo, Notre DameNotre Dame
Mark Vidal, Mark Vidal, DanaDana--Farber, HarvardFarber, Harvard
Michael E. Cusick, Michael E. Cusick, 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
Juyong Park, Juyong Park, Northeastern University & DFNortheastern University & DF
Zoltan N. Oltvai, Zoltan N. Oltvai, Pitssburgh Medical SchoolPitssburgh Medical School
Dashun Wang, Dashun Wang, Northeastern UniversityNortheastern University
Top Related