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

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

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

5. Internet-Map

6. Origin of SF networks: Growth and preferential attachment Barabási & Albert, Science 286, 509 (1999) P(k) ~k -3 BA model (1) Networks continuously expand by the addition of new nodes WWW : addition of new documents 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. (2) New nodes prefer to link to highly connected nodes. WWW : linking to well known sites

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

8. Robustness Complex systems maintain their basic functions even under errors and failures (cell  mutations; Internet  router breakdowns) node failure fcfc 01 Fraction of removed nodes, f 1 S Robustness

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

10. Don’t forget the movie again! 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. 0 km300 km100 km200 km 0 km 100 km 200 km Mobile Phone Users

16. Two possible explanations 1. Each users follows a Lévy flight 2. The difference between individuals follows a power law β=1.75±0.15 Δr: jump between consecutive recorded locations.

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

18. Time dependence of human mobility Radius of Gyration:

19. β r =1.65±0.15 Scaling in human trajectories

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

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

23. The shape of human trajectories

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