Toward a Universal Understanding of Human Mobility and Social Networks 胡延庆 郇迪 张江 黎勇 樊瑛 王有贵 狄增如 北京师范大学管理学院系统科学系北京师范大学复杂性研究中心 苏州 苏州

Background and Motivation Empirical Results of Mobility Empirical Results of Mobility –Animals and Human Beings –Understanding Why Social Networks Social Networks –Distance Distribution of Social Links –Maximum Entropy Yields It Toward Universal Understanding of Both Mobility and Social Networks Toward Universal Understanding of Both Mobility and Social Networks

Mobility Pattern Pattern: most of the studies on animal mobility pattern including experimental data and theoretic analysis found that their mobility pattern follow the Levy flight: Levy flight search patterns of wandering albatrosses, Nature 381, (1996) Revisiting Le´vy flight search patterns of wandering albatrosses, bumblebees and deer, NATURE| Vol 449|25 October 2007 Scaling laws of marine predator search behaviour, Nature (2008 )

Human Mobility D. Brockmann, L. Hufnagel and T. Geisel, The scaling laws of human travel, Nature, 439, , (2006)

Human Mobility 1.75 Understanding individual human mobility patterns Marta C. Gonza´lez, Ce´sar A. Hidalgo & Albert-La´szlo´ Baraba´si, NATURE| Vol 453|5 June 2008

Optimizing the success of random searches G. M. Viswanathan*²³, Sergey V. Buldyrev*, Shlomo Havlin*§, M. G. E. da Luzk¶, E. P. Raposok# & H. Eugene Stanley*, NATURE |VOL 401 | 28 OCTOBER 1999 | Fish in Lévy-flight foraging Gandhimohan M. Viswanathan Lévy flights are a theoretical construct that has attracted wide interdisciplinary interest. Empirical evidence shows that the principle applies to the foraging of marine predators. NATURE|Vol 465|24 June 2010 Understanding Why

Search Efficiency Number of target Sites Visited to the Total Distance Tranversed

Exploration and Preferential return (i) Exploration: with probability the individual moves to a new location (ii) Preferential return: with probability

Complex Networks complex networks are the backbone of complex systems complex networks are the backbone of complex systems –every complex system is a network of interaction among numerous smaller elements –understanding a complex system = break down into parts + reassemble network anatomy is important to characterize because structure affects function (and vice-versa) network anatomy is important to characterize because structure affects function (and vice-versa) –ex: structure of social networks prevent spread of diseases prevent spread of diseases control spread of information (marketing, fads, rumors, etc.) control spread of information (marketing, fads, rumors, etc.)

Binary Network: Node----Link Binary Network: Node----Link –Weighted Network Link weight Link weight –Spatial Network Geometrical or Geographical Structure Geometrical or Geographical Structure

Spatial Properties of Social Networks Discovering What Discovering What Understanding Why Understanding Why Investigating Its Impacts Investigating Its Impacts –Navigability –Synchronization –Traffic Dynamics –Epidemic Process

Distance Is Not Dead: Social Interaction and Geographical Distance in the Internet era

Empirical Results D.Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins. PNAS 102, , (2005).

Empirical results R. Lambiotte and his cooperators: 2.5 million cooperators: 2.5 million mobile phone customers mobile phone customers Physica A. 387(2008) P(d)~ d^-1 The distribution of geographic distance between friends is

Investigating its Effects ----Navigation Social Networks Milgram: Six degrees of separation. Travers, J. and Milgram, S., Sociometry. 32, (1969).Kleinberg: Kleinberg, J. M. Navigation in a small world. Nature. in a small world. Nature. 406, 845 (2000)

Synchronization Synchronizability

Topology

Traffic Dynamics

Getting information through social network Getting information through social network Understanding Why Do the Networks Possess Spatial Scaling Properties

Maximization of Entropy α?α?

W=cL 下的理论分析  >1  <1

Mobility & Network Mobility & Network One Levy FlightsInfinit Levy Flights

Home-Return Effect Human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic travel distance and a significant probability to return to a few highly frequented locations.

Home-Return Effect

Concluding Remarks Social Networks >> Mobility Social Networks >> Mobility Maximization of Information Entropy Maximization of Information Entropy Home-Return Effect Home-Return Effect Universal Description of Levy Flight Universal Description of Levy Flight

谢谢大家！