Temporal Distance Metrics for Network Analysis

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TemporalDistanceMetricsforNetworkAnalysis

WorkwithMircoMusolesi,CeciliaMascolo&VitoLatora

JohnTang

Computer Laboratory

Mo6va6on

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Mo6va6on

Shortestpath(A,G)=[A,B,D,E,G]Shortestpathlength(A,G)=4hops

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Mo6va6on

•  Assump6ons– Linksalwaysavailable?– Nodesalwaysavailable?– Concurrentlyavailable?

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RealNetworks

Node Edges

SocialNetwork People Mee6ngs

ComputerNetwork Router Links

EcologicalFoodNetwork Species Predator‐prey

TrafficNetwork TrafficLightJunc6on Roads

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Sta6cGraph

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TemporalGraph

t=1 t=2 t=3

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TemporalGraph

• Sta6c• Shortestpath(A,G)=[A,B,D,E,G]• Shortestpathlength(A,G)=4hops

• Temporal• Shortestpath(A,G)=[A,C,B,D,E,F,G]• Shortestpathlength(A,G)=7hops• Time=3seconds

t=1 t=2 t=3

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Recap

•  Sta6cAnalysisisinsufficient•  TemporalProper6es

– Timeorder

– Dura6on– Frequency

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Recap

•  Sta6cAnalysisisinsufficient•  TemporalProper6es

– Timeorder

– Dura6on– Frequency

•  Anydifferenceinrealnetworktraces?

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TemporalMetrics

•  ShortestTemporalPathLength

•  ShortestPathwithtemporalconstraints

•  TemporalEfficiency

dij =

d∗ij =

Eij =1

dij

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TemporalMetrics

•  AverageTemporal

•  AverageTemporal

•  AverageEfficiency

L = 1N(N−1)

∑ij dij

L∗ = 1N(N−1)

∑ij d∗ij

Eglob = 1N(N−1)

∑ij Eij

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Evalua6on

•  Infocom2005

•  Bluetoothcoloca6onscans•  5MinuteWindows

•  Measure24hoursstar6ng12am

Sta=c Temporal

Day N <k> Ac=vity Contacts L Eglob L* L Eglob

1 37 25.73 6pm‐12pm 3668 1.291 0.856 4.090 19h39m 0.003

2 39 28.31 12am‐12pm 8357 1.269 0.870 4.556 9h6m 0.024

3 38 22.32 12am‐12pm 4217 1.420 0.798 4.003 10h32m 0.018

4 39 21.44 12am‐5pm 3024 1.444 0.781 4.705 9h55m 0.013

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Conclusions

•  Sta6c– Overes6mateavailablehops

– Underes6matesshortestpaths

•  Temporal– Timeorder–  Indica6onof6me

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Contact

john.tang@cl.cam.ac.uk

www.cl.cam.ac.uk/~jkt27

J.Tang,M.Musolesi,C.Mascolo,V.Latora,“TemporalDistanceMetricsforSocialNetworkAnalysis”,ACMSIGCOMMWOSN09.August2009.