Walter WillingerAT&T Research Labs

Reza Rejaie, Mojtaba Torkjazi, Masoud ValafarUniversity of Oregon

Mauro MaggioniDuke University

HotMetrics’09, Seattle WA

MotivationOnline Social Networks (OSNs) are becoming increasingly

popular over the InternetThis growing popularity has motivated researchers to

characterize user connectivity and user interaction in OSNsExample: Facebook

Launched in 2004 and opened up to the general public in 2006 More than 200M users as of Early 2009 and 300K new users per

day By late 2008, 300K images per second and 10 billion photos in

total Characterizing OSNs is critical for

Developing measurement and performance modeling/analysis tools

Improving OSN network architecture and system design Understanding privacy and user behavior

Much of the existing OSN research studies seems to have lost sight of this unique opportunity for characterizing OSNs

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State-of-the-art in OSN CharacterizationMain focus has been on

Simple connectivity structures (e.g. friendship graphs or interaction graphs)

Graph metrics such as node degree distribution, clustering coefficient, density, diameter

Little is known about the actual structure and dynamics User arrival/departure to/from the system User interactionsGrowth rate of the system

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This PaperWe argue that OSN research has to change

courseAbandon the traditional treatment of OSNs as

static networks and become serious about dealing with dynamic nature of real OSNs

Come up with new techniques/tools for collecting and analyzing relevant data

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Static Friendship Graph Caveat emptor: our toy examples are for illustration purposes only,

they are not meant to describe real-world OSNs Toy example of static friendship graph (TOYFB)

Hierarchical Scale-Free networks [Barabasi2002] HSF(n, m), n: size of the cell, m: number of levels

HSF graphs show power law node degree distribution, rich local clustering properties, and well-defined cluster-within-cluster structure

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Step 1: HSF(5,0)

Step 2: HSF(5,1)

Step 3: HSF(5,2)

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Dynamic Friendship Graph (I)

Show a very elementary and highly stylized evolutionary process125 users join our toy OSN over timeBecome friends with other users over timeBecome inactive after a while

Consider time interval [0, 1], where graph structure changes at time points 1/16, 2/16, ..., and 16/16At any of these discrete points, some friendship

relations become inactive, and some new friendships are being established

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t = 1/16

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t = 2/16

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t = 3/16

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t = 4/16

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t = 5/16

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t =6/16

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t = 7/16

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t = 8/16

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t = 9/16

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t = 10/16

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t = 11/16

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t = 12/16

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t = 13/16

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t = 14/16

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t = 15/16

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t = 16/16

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Dynamic Friendship Graph (III) A full crawl of TOYFB is identical to HSF(5,2), since friend lists

maintained by users do not reflect any de-activation of friendship relations Properties of the temporal snapshots , TOYFB(t), are radically different

from those of the static counterpart TOYFB What are the effective and efficient methods for accurately capturing and

systematically characterizing the dynamic nature of large-scale real-world OSNs?

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Measurement - StaticCrawling complete snapshots does not scale

Limited rate of crawling (e.g. 10 query/sec in Flickr)

Large population of OSNs (millions of users)Partial snapshot is likely to be distorted and

biased towards high degree nodes Graph sampling is a promising approach for

characterizing node properties [Stutzbach2006, Rasti2009]

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Measurement - DynamicGoal of sampling: collect a “representative” set

of usersIn an unknown graph changing underneath any

measurement tool (e.g. crawler), what does “representative” mean?

Even with a solid definition for “representative” snapshot, how to develop appropriate sampling techniques to deal with dynamic nature of OSNs?

Knowing all the challenges for measuring OSNs, is there any innovative approach for future analysis?

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Analysis (I)A new approach based on the following two observations in

OSNsClustering at different spatial scales Faster and more noisy temporal dynamics at finer levels of

resolutions of the graphMulti-Resolution Analysis (MRA) for graphs

Start from a coarse-scale representation that is typically small in size and has a slow dynamics

Use the insight gained at this scale to study the graph at the next finer levels of resolutions

Diffusion Wavelets (DW) as a principled approach for graph MRADW provides the necessary mathematical framework for

performing the above graph coarsening intuition [Maggioni2004]

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Analysis (II)TOYFB at scale 2 is smaller in size than TOYFB at scale 1TOYFB at scale 2 has slower dynamics than TOYFB at scale 1

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Scale 1

Scale 2

Scale 3

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t = 1/16

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t = 5/16

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t = 9/16

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t = 13/16

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ConclusionStop ignoring the dynamic nature of OSNsFor a better understanding of OSNs

Abandon current traditional measurement, modeling, analysis, and validation approaches

Replace them by new techniques that can account for the most of the dynamic features of real-world OSNs

New methodologies are required for advancingOSN measurement: extend and develop current

graph sampling techniques to consider churn in OSNs

OSN analysis: apply Multi-Resolution Analysis (MRA) methodology for large-scale dynamic graph structures

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