Stefano Boccaletti Complex networks in science and society

Stefano Boccaletti Complex 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 Garcia PAMPLONA 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? v 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) Six Degrees of Separation John Guare Social networks: Many individuals with diverse social interactions between them.

Communication networks The Earth is developing an electronic nervous system, a network with diverse nodes and links are -computers -phone lines -routers -TV cables -satellites -EM waves

INTERNET BACKBONE

Erdös-Rényi model (1960) Pál Erdös (1913 -1996) Poisson distribution Connect with probability p

ARE COMPLEX NETWORKS REALLY RANDOM?

Road and Airline networks Poisson distribution Exponential Network Power-law distribution Scale-free Network

SCIENCE CITATION INDEX Nodes: papers Links: citations 25 Witten-Sander PRL 1981 2212 P(k) ~k-

SCIENCE COAUTHORSHIP Nodes: scientist (authors) Links: write paper together

ACTOR CONNECTIVITIES Nodes: 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

Centrality: Why Kevin Bacon? Measure the average distance between Kevin Bacon and all other actors. No. of movies : 46 No. of actors : 1811 Kevin Bacon Average separation: 2. 79 Is Kevin Bacon the most connected actor? NO! 876 Kevin Bacon 2. 786981 46 1811

#1 Rod Steiger #876 Kevin Bacon #2 Donald Pleasence #3 Martin Sheen

FOOD WEBS Nodes: trophic species Links: trophic interactions R. J. Williams, N. D. Martinez Nature (2000)

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 I Nodes: proteins Links: physical P. Uetz, et al. Nature 403, 623 -7 (2000). interactions (binding)

Protein networks II 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 p 53 network is to compare it to the Internet. The cell, like the Internet, appears to be a ‘scale-free network’. ”

p 53 network (mammals)

Watts-Strogatz Model (Watts and Strogatz, Nature 393, 440 (1998)) C(p) : clustering coeff. L(p) : average path length

BA - Scale-free model (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 A. -L. Barabási, R. Albert, Science 286, 509 (1999)

Robustness Complex systems maintain their basic functions even under errors and failures (cell mutations; Internet router breakdowns) 1 S fc 0 1 Fraction of removed nodes, f node failure

Achilles’ Heel of complex networks failure attack Internet 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)