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
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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)