Minas Gjoka, UC IrvineWalking in Facebook*Walking in Facebook:A Case Study of Unbiased Sampling of OSNs

Minas Gjoka, Maciej Kurant , Carter Butts, Athina Markopoulou UC Irvine, EPFL

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Minas Gjoka, UC IrvineWalking in Facebook*OutlineMotivation and Problem StatementSampling MethodologyData AnalysisConclusion

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Minas Gjoka, UC IrvineWalking in Facebook*Online Social Networks (OSNs) A network of declared friendships between users

Allows users to maintain relationships

Many popular OSNs with different focusFacebook, LinkedIn, Flickr,

Social Graph

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Minas Gjoka, UC IrvineWalking in Facebook*Why Sample OSNs?Representative samples desirablestudy propertiestest algorithms

Obtaining complete dataset difficultcompanies usually unwilling to share data tremendous overhead to measure all (~100TB for Facebook)

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Minas Gjoka, UC IrvineWalking in Facebook*Problem statementObtain a representative sample of users in a given OSN by exploration of the social graph. in this work we sample Facebook (FB)explore graph using various crawling techniques

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Minas Gjoka, UC IrvineWalking in Facebook*Related WorkGraph traversal (BFS)A. Mislove et al, IMC 2007Y. Ahn et al, WWW 2007C. Wilson, Eurosys 2009Random walks (MHRW, RDS)M. Henzinger et al, WWW 2000D. Stutbach et al, IMC 2006A. Rasti et al, Mini Infocom 2009

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Minas Gjoka, UC IrvineWalking in Facebook*Our ContributionsCompare various crawling techniques in FBs social graph Breadth-First-Search (BFS)Random Walk (RW)Metropolis-Hastings Random Walk (MHRW)

Practical recommendationsonline convergence diagnostic testsproper use of multiple parallel chainsmethods that perform better and tradeoffs

Uniform sample of Facebook userscollection and analysismade available to researchers

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Minas Gjoka, UC IrvineWalking in Facebook*OutlineMotivation and Problem StatementSampling Methodologycrawling methodsdata collectionconvergence evaluationmethod comparisonsData AnalysisConclusion

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Minas Gjoka, UC IrvineWalking in Facebook*(1) Breadth-First-Search (BFS)Starting from a seed, explores all neighbor nodes. Process continues iteratively without replacement.

BFS leads to bias towards high degree nodes Lee et al, Statistical properties of Sampled Networks, Phys Review E, 2006

Early measurement studies of OSNs use BFS as primary sampling techniquei.e [Mislove et al], [Ahn et al], [Wilson et al.]

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Minas Gjoka, UC IrvineWalking in Facebook*(2) Random Walk (RW)Explores graph one node at a time with replacement

In the stationary distribution

Degree of node Number of edges

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Minas Gjoka, UC IrvineWalking in Facebook*(3) Re-Weighted Random Walk (RWRW) Hansen-Hurwitz estimator Corrects for degree bias at the end of collection

Without re-weighting, the probability distribution for node property A is:

Re-Weighted probability distribution :

Subset of sampled nodes with value iAll sampled nodesDegree of node u

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Minas Gjoka, UC IrvineWalking in Facebook*(4) Metropolis-Hastings Random Walk (MHRW)Explore graph one node at a time with replacement

In the stationary distribution

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Minas Gjoka, UC IrvineWalking in Facebook*Uniform userID Sampling (UNI)As a basis for comparison, we collect a uniform sample of Facebook userIDs (UNI)rejection sampling on the 32-bit userID space

UNI not a general solution for sampling OSNsuserID space must not be sparsenames instead of numbers

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Minas Gjoka, UC IrvineWalking in Facebook*Summary of Datasets

Egonets for a subsample of MHRW- local properties of nodes

Datasets available at: http://odysseas.calit2.uci.edu/research/osn.html

Sampling methodMHRWRWBFSUNI#Valid Users28x81K28x81K28x81K984K# Unique Users957K2.19M2.20M984K

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Minas Gjoka, UC IrvineWalking in Facebook*Data CollectionBasic Node InformationWhat information do we collect for each sampled node u?

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UserIDName NetworksPrivacy settings

UserIDName NetworksPrivacy settings

Friend ListUserIDNameNetworksPrivacy Settings

UserIDName NetworksPrivacy settings

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Regional School/Workplace

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Minas Gjoka, UC IrvineWalking in Facebook*Detecting Convergence

Number of samples (iterations) to loose dependence from starting points?

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Minas Gjoka, UC IrvineWalking in Facebook*Online Convergence DiagnosticsGewekeDetects convergence for a single walk. Let X be a sequence of samples for metric of interest.

J. Geweke, Evaluating the accuracy of sampling based approaches to calculate posterior moments in Bayesian Statistics 4, 1992Xa

Xb

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Minas Gjoka, UC IrvineWalking in Facebook*Online Convergence DiagnosticsGelman-RubinDetects convergence for m>1 walks

A. Gelman, D. Rubin, Inference from iterative simulation using multiple sequences in Statistical Science Volume 7, 1992Walk 1Walk 2Walk 3Between walksvarianceWithin walksvariance

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Minas Gjoka, UC IrvineWalking in Facebook*When do we reach equilibrium?Burn-in determined to be 3K

Node Degree

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Minas Gjoka, UC IrvineWalking in Facebook*Methods ComparisonNode DegreePoor performance for BFS, RW

MHRW, RWRW produce good estimates per chainoverall28 crawls

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Minas Gjoka, UC IrvineWalking in Facebook*Sampling BiasBFSLow degree nodes under-represented by two orders of magnitude

BFS is biased

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Minas Gjoka, UC IrvineWalking in Facebook*Sampling Bias MHRW, RW, RWRWDegree distribution identical to UNI (MHRW,RWRW)RW as biased as BFS but with smaller variance in each walk

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Minas Gjoka, UC IrvineWalking in Facebook*Practical Recommendations for Sampling MethodsUse MHRW or RWRW. Do not use BFS, RW.

Use formal convergence diagnosticsassess convergence onlineuse multiple parallel walks

MHRW vs RWRWRWRW slightly better performanceMHRW provides a ready-to-use sample

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Minas Gjoka, UC IrvineWalking in Facebook*OutlineMotivation and Problem StatementSampling MethodologyData AnalysisConclusion

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Minas Gjoka, UC IrvineWalking in Facebook*FB Social GraphDegree DistributionDegree distribution not a power law

a2=3.38a1=1.32

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Minas Gjoka, UC IrvineWalking in Facebook*FB Social GraphTopological Characteristics

Our MHRW sample Assortativity Coefficient = 0.233range of Clustering Coefficient [0.05, 0.35]

[Wilson et al, Eurosys 09] Assortativity Coefficient = 0.17range of Clustering Coefficient [0.05, 0.18]

More details in our paper and technical report

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Minas Gjoka, UC IrvineWalking in Facebook*ConclusionCompared graph crawling methodsMHRW, RWRW performed remarkably wellBFS, RW lead to substantial bias

Practical recommendationscorrect for biasusage of online convergence diagnosticsproper use of multiple chains

Datasets publicly availablehttp://odysseas.calit2.uci.edu/research/osn.html

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Minas Gjoka, UC IrvineWalking in Facebook*

Thank you Questions?

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