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Computer Laboratory
TemporalDistanceMetricsforNetworkAnalysis
WorkwithMircoMusolesi,CeciliaMascolo&VitoLatora
JohnTang
Computer Laboratory
Mo6va6on
Computer Laboratory
Mo6va6on
Shortestpath(A,G)=[A,B,D,E,G]Shortestpathlength(A,G)=4hops
Computer Laboratory
Mo6va6on
• Assump6ons– Linksalwaysavailable?– Nodesalwaysavailable?– Concurrentlyavailable?
Computer Laboratory
RealNetworks
Node Edges
SocialNetwork People Mee6ngs
ComputerNetwork Router Links
EcologicalFoodNetwork Species Predator‐prey
TrafficNetwork TrafficLightJunc6on Roads
Computer Laboratory
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
Computer Laboratory
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
Computer Laboratory
Contact
www.cl.cam.ac.uk/~jkt27
J.Tang,M.Musolesi,C.Mascolo,V.Latora,“TemporalDistanceMetricsforSocialNetworkAnalysis”,ACMSIGCOMMWOSN09.August2009.
