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管理学院系统科学系北京师范大学复杂性研究中心北京师范大学复杂性研究中心 2010.10 2010.10 苏州苏州

Background and Background and MotivationMotivation Empirical Results of MobilityEmpirical Results of Mobility

– Animals and Human BeingsAnimals and Human Beings– Understanding WhyUnderstanding Why

Social NetworksSocial Networks– Distance Distribution of Social LinksDistance Distribution of Social Links– Maximum Entropy Yields ItMaximum Entropy Yields It

Toward Universal Understanding of Toward Universal Understanding of Both Mobility and Social NetworksBoth Mobility and Social Networks

Mobility PatternMobility PatternPattern: 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 2007Scaling laws of marine predator search behaviour, Nature (2008 )

2)Pr( dd

Human MobilityHuman Mobility

D. Brockmann, L. Hufnagel and T. Geisel, The scaling laws of human travel, Nature, 439, 462-465, (2006).

-1.59

Human MobilityHuman Mobility 1.75

Understanding individual human mobility patternsMarta C. Gonza´lez, Ce´sar A. Hidalgo & Albert-La´szlo´ Bara

ba´si, NATURE| Vol 453|5 June 2008

Optimizing the success of random searchesG. 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 princi

pleapplies to the foraging of marine

predators.NATURE|Vol 465|24 Ju

ne 2010

Understanding Why

Search EfficiencyNumber of target Sites Visited

to the Total Distance Tranversed

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

Complex NetworksComplex Networks complex networks are the backbone of complex networks are the backbone of

complex systemscomplex systems– every complex system is a network of every complex system is a network of

interaction among numerous smaller elements interaction among numerous smaller elements – understanding a complex system = break down understanding a complex system = break down

into parts + reassemble into parts + reassemble network anatomy is important to network anatomy is important to

characterize because structure affects characterize because structure affects function (and vice-versa)function (and vice-versa)– ex: structure of social networksex: structure of social networks

prevent spread of diseasesprevent spread of diseases control spread of information (marketing, fads, rumors, etc.)control spread of information (marketing, fads, rumors, etc.)

Binary Network: Node----LinkBinary Network: Node----Link– Weighted NetworkWeighted Network

Link weightLink weight

– Spatial NetworkSpatial Network Geometrical or Geographical StructureGeometrical or Geographical Structure

Spatial Properties of Spatial Properties of Social NetworksSocial Networks

Discovering WhatDiscovering What Understanding WhyUnderstanding Why Investigating Its ImpactsInvestigating Its Impacts

– NavigabilityNavigability– SynchronizationSynchronization– Traffic DynamicsTraffic Dynamics– Epidemic ProcessEpidemic Process

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

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

Empirical ResultsEmpirical Results

D.Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins. PNAS 102, 11623-11628, (2005).

Empirical resultsEmpirical resultsR. Lambiotte and hisR. Lambiotte and his cooperatorscooperators: : 2.5 million2.5 million mobile phone customersmobile phone customersPhysica APhysica A. 387(2008). 387(2008)

P(d)~ d^-1

The distribution of geographic distance between friends is

Investigating its EffectsInvestigating its Effects ----Navigation ----Navigation Social NetworksSocial Networks

Milgram: Six degrees of separation.Milgram: Six degrees of separation.Travers, J. and Milgram, S., Travers, J. and Milgram, S., SociometrySociometry. 32, 425-443 . 32, 425-443 (1969).(1969).

Kleinberg:Kleinberg:Kleinberg, J. M. NavigationKleinberg, J. M. Navigation in a small world. in a small world. NatureNature. . 406, 845 (2000)406, 845 (2000)

SynchronizationSynchronization

SynchronizabilitySynchronizability

TopologyTopology

Traffic DynamicsTraffic Dynamics

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Getting Getting information information through social through social networknetwork

Understanding Why Do the Understanding Why Do the Networks Possess Spatial Networks Possess Spatial Scaling PropertiesScaling Properties

Understanding Why Do the Understanding Why Do the Networks Possess Spatial Scaling Networks Possess Spatial Scaling PropertiesProperties

Maximization of Entropy

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One Levy FlightsInfinit Levy Flights

Home-Return EffectHome-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 EffectHome-Return Effect

Concluding RemarksConcluding Remarks Social Networks >> MobilitySocial Networks >> Mobility Maximization of Information Maximization of Information

EntropyEntropy Home-Return EffectHome-Return Effect Universal Description of Levy Universal Description of Levy

FlightFlight

谢谢大家！谢谢大家！