Multigraph Sampling of Online Social Networks Minas Gjoka, Carter Butts, Maciej Kurant, Athina Markopoulou 1Multigraph sampling.

Multigraph Sampling of Online Social Networks

Minas Gjoka, Carter Butts, Maciej Kurant, Athina Markopoulou

1Multigraph sampling

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 )

Multigraph sampling Minas Gjoka

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