Stefano BoccalettiComplex networks in science and society

*Istituto Nazionale di Ottica Applicata - Largo E. Fermi, 6 - 50125 Florence, ITALY

*CNR-Istituto dei Sistemi Complessi

* MIND- Mediterranean Institute for Nonlinear Dynamics

Coworkers:Dong-Uk Hwang, Mario Chavez, Andreas Amann,Vito latora Hector Mancini, Jean Bragard, Louis Pecora, Juergen Kurths

Dedicated to the memory of Carlos Pérez GarciaPAMPLONA 2005

Summary

•WHAT IS A NETWORK?

•WHAT IS A COMPLEX NETWORK?

•THE STRUCTURE OF COMPLEX NETWORKS

•THE MODELS OF COMPLEX NETWORKS

Do you want to know more? S.Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang

COMPLEX NETWORKS: STRUCTURE AND DYNAMICS

212 pages, 856 References

TO APPEAR SOON IN PHYSICS REPORTS

For preprints write to stefano@ino.it

Society

Nodes: individuals

Links: social relationship (family/work/friendship/etc.)

S. Milgram (1967)

John Guare Six Degrees of Separation

Social networks: Many individuals with diverse social interactions between them.

Communication networksThe Earth is developing an electronic nervous system, a network with diverse nodes and links are

-computers

-routers

-satellites

-phone lines

-TV cables

-EM waves

INTERNET BACKBONE

Erdös-Rényi model (1960)

Pál ErdösPál Erdös (1913-1996)

Connect with probability p

Poisson distribution

ARE COMPLEX NETWORKS REALLY RANDOM?

Road and Airline networksPoisson distribution

Exponential Network

Power-law distribution

Scale-free Network

SCIENCE CITATION INDEX

Nodes: papers Links: citations

P(k) ~k-2212

25

Witten-Sander

PRL 1981

SCIENCE COAUTHORSHIP

Nodes: scientist (authors)

Links: write paper together

ACTOR CONNECTIVITIESNodes: actors Links: cast jointly

Days of Thunder (1990) Far and Away

(1992) Eyes Wide Shut (1999)

N = 212,250 actors k = 28.78

P(k) ~k-

=2.3

Rank NameAveragedistance

# ofmovies

# oflinks

1 Rod Steiger 2.537527 112 25622 Donald Pleasence 2.542376 180 28743 Martin Sheen 2.551210 136 35014 Christopher Lee 2.552497 201 29935 Robert Mitchum 2.557181 136 29056 Charlton Heston 2.566284 104 25527 Eddie Albert 2.567036 112 33338 Robert Vaughn 2.570193 126 27619 Donald Sutherland 2.577880 107 2865

10 John Gielgud 2.578980 122 294211 Anthony Quinn 2.579750 146 297812 James Earl Jones 2.584440 112 3787…

876 Kevin Bacon 2.786981 46 1811…

Centrality: Why Kevin Bacon?Measure the average distance between Kevin Bacon and all other actors.

No. of movies : 46 No. of actors : 1811 Average separation: 2.79Kevin Bacon

Is Kevin Bacon the most

connected actor?

NO!

876 Kevin Bacon 2.786981 46 1811

Rod Steiger

Martin Sheen

Donald Pleasence

#1

#2

#3

#876Kevin Bacon

FOOD WEBS

R.J. Williams, N.D. Martinez Nature (2000)

Nodes: trophic species

Links: trophic interactions

SEX WEBS

Nodes: people (Females; Males) Links: sexual relationships

4781 Swedes; 18-74;

59% response rate.

Liljeros et al. Nature 2001

Metabolic Networks I

Nodes: chemicals (substrates) Links: bio-chemical reactions

Metabolic Networks II

Archaea Bacteria Eukaryotes

Organisms from all three domains of life are scale-free networks!

H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000)

Protein networks INodes: proteins Links: physical interactions (binding)

P. Uetz, et al. Nature 403, 623-7 (2000).

Protein networks II

)exp()(~)( 00

k

kkkkkP

H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

Nature 408 307 (2000)

…

“One way to understand the p53 network is to compare it to the Internet.

The cell, like the Internet, appears to be a ‘scale-free network’.”

p53 network (mammals)

Network C Crand L N

WWW 0.1078 0.00023 3.1 153127

Internet 0.18-0.3 0.001 3.7-3.76 3015-6209

Actor 0.79 0.00027 3.65 225226

Coauthorship 0.43 0.00018 5.9 52909

Metabolic 0.32 0.026 2.9 282

Foodweb 0.22 0.06 2.43 134

C. elegance 0.28 0.05 2.65 282

WWW(in)

Internet ActorCitation

indexSexWeb

Cellularnetwork

Phone callnetwork

linguistics

= 2.1 = 2. 5 = 2.3 = 3 = 3.5 = 2.1 = 2.1 = 2.8

Watts-Strogatz Model

C(p) : clustering coeff. L(p) : average path length

(Watts and Strogatz, Nature 393, 440 (1998))

BA - Scale-free model

A.-L.Barabási, R. Albert, Science 286, 509 (1999)

(1) GROWTH : At every timestep we add a new node with m edges (connected to the nodes already present in the system).

(2) PREFERENTIAL ATTACHMENT : The probability Π that a new node will be connected to node i depends on the connectivity ki of that node

P(k) ~k-3

Robustness

Complex 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

Achilles’ Heel of complex networks

Internet

failure

attack

R. Albert, H. Jeong, A.L. Barabasi, Nature 406 378 (2000)

Yeast protein network- lethality and topological position -

Highly connected proteins are more essential (lethal)...

H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)