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Human Travel Patterns
Albert-László BarabásiAlbert-László Barabási
Center for Complex Networks Research, Northeastern U.Center for Complex Networks Research, Northeastern U.
Department of Medicine, Harvard U.Department of Medicine, Harvard U.
BarabasiLab.com
Tropical forest in Yucatan, Mexico
“Lévy flight” by a spider monkey
Animal MotionAnimal Motion
Vishwanatan et. al. Nature (1996); Nature (1999).
Wandering AlbatrossWandering Albatross
Wandering AlbatrossWandering Albatross
Sims et al. Nature (2008).
1 Jun
22 Jun
24 May
7 Aug
11 Jul
28 Jul
5 Jan
10 Oct
24 Nov
Basking shark
Porbeagle shark Sims et al. Nature (2008).
Random Walks Lévy flights
Human MotionHuman Motion
Brockmann et. al. Nature (2006)
A real human trajectory
Mobile Phone Users
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Data Collection Limitations
We know only the tower the user communicates with, not the real location.
We know the location (tower) only when the user makes a call.
Interevent times are bursty (non-Poisson process—Power law interevent time distribution).
ALB, Nature 2005.
CCNRCCNR
Interevent TimesInterevent Times
J. Candia et al.
A-L. B, Nature 2005.
0 km 300 km100 km 200 km
0 km
100
km
200
km
Mobile Phone Users
Two possible explanations
1.Each users follows a Lévy flight
2.The difference between individuals follows a power law
β=1.75±0.15
Understanding human trajectoriesUnderstanding human trajectories
Radius of Radius of Gyration:Gyration:
Center of Mass:Center of Mass:
Characterizing human trajectoriesCharacterizing human trajectories
Radius of Radius of Gyration:Gyration:
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Characterizing human trajectoriesCharacterizing human trajectories
Radius of Radius of Gyration:Gyration:
βr=1.65±0.15
Scaling in human trajectoriesScaling in human trajectories
0 km 300 km100 km 200 km
0 km
100
km
200
km
Mobile Phone Users
β=1.75±0.15βr=1.65±0.15
Scaling in human trajectoriesScaling in human trajectories
α=1.2
Relationship between exponentsRelationship between exponents
Jump size distribution P(Δr)~(Δr)-β represents a convolution between
*population heterogeneity P(rg)~rg-βr
*Levy flight with exponent α truncated by rg
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Return time distributionsReturn time distributions
Mobile Phone Users
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The shape of human trajectoriesThe shape of human trajectories
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The shape of human trajectoriesThe shape of human trajectories
Mobile Phone Viruses
Hypponen M. Scientific American Nov. 70-77 (2006).
Spreading mechanism for cell phone viruses
Short range infection process(similar to biological viruses, like influenza or SARS)
Long range infection process(similar to computer viruses)
Palla, A.-L. B & Vicsek (2007).Onella et al, PNAS (2007)
Social Network (MMS virus)
González, Hidalgo and A-L.B.,
Nature 453, 779 (2008)
Human Motion(Bluetooth virus)
MMS and Bluetooth Viruses
Spatial Spreading Patterns of Bluetooth and MMS virus
Spatial Spreading patterns of Bluetooth and MMS viruses
Bluetooth Virus MMS Virus
Driven by Human Mobility:Slow, but can reach all users with time.
Driven by the Social Network:Fast, but can reach only a finite fraction of users (the giant component).
What is the origin of this saturation?
Spreading mechanism for cell phone viruses
If the market share of an Operating Systemis under mc~10%, MMS
viruses cannot spread.
0 km 300 km100 km 200 km
0 km
100
km
200
km
Mobile Phone Users
Pu Wang Cesar Hidalgo
CollaboratorsCollaborators
Marta Gonzalez
www.BarabasiLab.com
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