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