Multigraph Sampling of Online Social Networks

Minas Gjoka, Carter Butts, Maciej Kurant, Athina Markopoulou

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Outline

• Multigraph sampling– Motivation– Sampling method– Internet Measurements– Conclusion

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Problem statement

• Obtain a representative sample of OSN users by exploration of the social graph.

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Multigraph sampling Minas Gjoka

Motivation for multiple relations

• Principled methods for graph sampling– Metropolis Hastings Random Walk– Re-weighted Random Walk

“Walking in Facebook: A Case Study of Unbiased Sampling of OSNs,” INFOCOM ‘10

• But..graph characteristics affect mixing and convergence

• fragmented social graph• highly clustered areas

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Fragmented social graph

5Union

Friendship

Event attendance

Group membershipMultigraph sampling

Largest Connected ComponentOther Connected Components

Highly clustered social graph

Friendship Event attendance

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Union

Multigraph sampling Minas Gjoka

Proposal

• Graph exploration using multiple user relations– perform random walk– re-weighting at the end of the walk– online convergence diagnostics applicable

• Theoretical benefits– faster mixing– discovery of isolated components

• Open questions– how to combine relations– implementation efficiency– evaluation of sampling benefits in a realistic scenario

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Friends

Events

Groups

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Friends

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deg(F, tot) = 8

deg(F, red) = 1

deg(F, blue) = 3

deg(F, green) = 4

G* = Friends + Events + Groups

( G* is a union multigraph )

Combination of multiple relations

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K G = Friends + Events + Groups

( G is a union graph )

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Multigraph samplingImplementation efficiency

Degree information available without enumeration

5)( Fd

8/1)( Friendsp

8/4)( Eventsp

8/3)( Groupsp

Take advantage of pages functionality 11

8)(* Fd

Multigraph sampling Minas Gjoka

Multigraph samplingInternet Measurements

• Last.fm, an Internet radio service– social networking features– multiple relations– fragmented graph components and highly clustered

users expected

• Last.fm relations used– Friends– Groups– Events– Neighbors

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Data CollectionSampled node information

• Crawling using Last.fm API and HTML scrapinguserIDcountryageregistration time…

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Summary of datasetsLast.fm - July 2010

Crawl type # Total Users % Unique Users

Friends 5x50K 71%

Events 5x50K 58%Groups 5x50K 74%Neighbors 5x50K 53%Friends-Events-Groups-Neighbors

5x50K 76%

UNI 500K 99%

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Comparison to UNI% of Subscribers

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% o

f Sub

scrib

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Last.fm Charts EstimationApplication of sampling

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Last.fm Charts EstimationArtist Charts

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Related Work

• Fastest mixing Markov Chain– Boyd et al - SIAM Review 2004

• Sampling in fragmented graphs– Ribeiro et al. Frontier Sampling – IMC 2010

• Last.fm studies– Konstas et al - SIGIR ‘09– Schifanella et al - WSDM ‘10

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Conclusion

• Introduced multigraph sampling– simple and efficient– discovers isolates components– better approximation of distributions and means– multigraph dataset planned for public release

• Future work on multigraph sampling– selection of relations– weighted relations

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Thank youQuestions?

Multigraph sampling Minas Gjoka