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S tefano Boccaletti Complex networks in science and society

S tefano 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:

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S tefano Boccaletti Complex networks in science and society

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  1. 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 Garcia PAMPLONA 2005

  2. Summary • WHAT IS A NETWORK? • WHAT IS A COMPLEX NETWORK? • THE STRUCTURE OF COMPLEX NETWORKS • THE MODELS OF COMPLEX NETWORKS

  3. 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

  4. Society Society Nodes: individuals Links: social relationship (family/work/friendship/etc.) S. Milgram (1967) Six Degrees of Separation John Guare Social networks: Many individuals with diversesocial interactions between them.

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

  6. INTERNET BACKBONE

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

  8. ARE COMPLEX NETWORKS REALLY RANDOM? NO!

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

  10. 25 2212 SCIENCE CITATION INDEX Nodes:papers Links:citations Witten-Sander PRL 1981 P(k) ~k-

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

  12. 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

  13. Bacon-list NO! 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: 2.79 Kevin Bacon Is Kevin Bacon the most connected actor?

  14. Bacon-map #876 Kevin Bacon #1 Rod Steiger Donald Pleasence #2 Martin Sheen #3

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

  16. SEX WEBS Nodes: people (Females; Males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. Liljeros et al. Nature 2001

  17. Metabolic Networks I Nodes: chemicals (substrates)Links: bio-chemical reactions

  18. 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)

  19. Protein networks I Nodes: proteins Links: physical interactions (binding) P. Uetz, et al.Nature403, 623-7 (2000).

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

  21. 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’.”

  22. p53 network (mammals)

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

  24. P(k) ~k-3 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 A.-L.Barabási, R. Albert, Science 286, 509 (1999)

  25. 1 node failure S fc 0 1 Fraction of removed nodes, f Robustness Complex systems maintain their basic functions even under errors and failures (cell  mutations; Internet  router breakdowns)

  26. Achilles Heel Achilles’ Heel of complex networks failure attack Internet R. Albert, H. Jeong, A.L. Barabasi, Nature 406 378 (2000)

  27. Prot- robustness 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)

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