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From Complex Networks to Human Travel Patterns

From Complex Networks to Human Travel Patterns. Albert-László Barabási Center for Complex Networks Research Northeastern University Department of Medicine and CCSB Harvard Medical School. www.BarabasiLab.com. Connect with probability p. p=1/6 N=10 k ~ 1.5. Poisson distribution.

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From Complex Networks to Human Travel Patterns

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  1. From Complex Networks to Human Travel Patterns Albert-László Barabási Center for Complex Networks Research Northeastern University Department of Medicine and CCSB Harvard Medical School www.BarabasiLab.com

  2. Connect with probability p p=1/6 N=10 k ~ 1.5 Poisson distribution Erdös-Rényi model(1960) Pál Erdös(1913-1996) - Democratic - Random

  3. WWW Expected P(k) ~ k- Found World Wide Web Nodes: WWW documents Links: URL links Over 10 billion documents Exponential Network ROBOT:collects all URL’s found in a document and follows them recursively Scale-free Network R. Albert, H. Jeong, A-L Barabási, Nature, 401 130 (1999).

  4. Internet INTERNET BACKBONE Nodes: computers, routers Links: physical lines (Faloutsos, Faloutsos and Faloutsos, 1999)

  5. Internet-Map

  6. Origin of SF networks: Growth and preferential attachment BA model (1) Networks continuously expand by the addition of new nodes WWW : addition of new documents (2) New nodes prefer to link to highly connected nodes. WWW : linking to well known sites P(k) ~k-3 GROWTH: add a new node with m links PREFERENTIAL ATTACHMENT:the probability that a node connects to a node with k links is proportional to k. Barabási & Albert, Science286, 509 (1999)

  7. Metab-movie Protein Interactions Metabolic Network Jeong, Tombor, Albert, Oltvai, & Barabási, Nature (2000); Jeong, Mason, Barabási &. Oltvai, Nature (2001); Wagner & Fell, Proc. R. Soc. B (2001)

  8. Robustness 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)

  9. Robust-SF Robustness of scale-free networks 1 S 0 1 f Attacks Failures   3 : fc=1 (R. Cohen et al PRL, 2000) fc Albert, Jeong, Barabási, Nature 406 378 (2000)

  10. Don’t forget the movie again!

  11. Human Motion Brockmann, Hufnagel, Geisel Nature (2006)

  12. Dollar Bill Motion Brockmann, Hufnagel, Geisel Nature (2006)

  13. A real human trajectory

  14. Mobile Phone Users

  15. Mobile Phone Users 200 km 100 km 0 km 0 km 100 km 200 km 300 km

  16. Δr: jump between consecutive recorded locations. β=1.75±0.15 • Two possible explanations • Each users follows a Lévy flight • The difference between individuals follows a power law Gonzales, Hidalgo, Barabasi, Nature 2008

  17. Understanding individual trajectories Center of Mass: Radius of Gyration:

  18. Time dependence of human mobility Radius of Gyration:

  19. Scaling in human trajectories βr=1.65±0.15 Gonzales, Hidalgo, Barabasi, Nature 2008

  20. Scaling in human trajectories β=1.75±0.15 βr=1.65±0.15 α=1.2

  21. Relationship between exponents Jump size distribution P(Δr)~(Δr)-βrepresents a convolution between *population heterogeneity P(rg)~rg-βr *Levy flight with exponent α truncated by rg

  22. The shape of human trajectories Gonzales, Hidalgo, Barabasi, Nature 2008

  23. Collaborators Pu Wang Marta Gonzalez Cesar Hidalgo www.BarabasiLab.com

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