1. Walter Willinger AT&T Research Labs Reza Rejaie, Mojtaba Torkjazi, Masoud Valafar University of Oregon Mauro Maggioni Duke University HotMetrics’09, Seattle WA

2. Motivation Online Social Networks (OSNs) are becoming increasingly popular over the Internet This growing popularity has motivated researchers to characterize user connectivity and user interaction in OSNs Example: 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 6/19/20092HotMetrics 2009 - Seattle WA

3. State-of-the-art in OSN Characterization Main 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 interactions Growth rate of the system 6/19/20093HotMetrics 2009 - Seattle WA

4. This Paper We argue that OSN research has to change course Abandon 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 6/19/20094HotMetrics 2009 - Seattle WA

5. 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 6/19/2009 Step 1: HSF(5,0) Step 2: HSF(5,1) Step 3: HSF(5,2) 5HotMetrics 2009 - Seattle WA

6. Dynamic Friendship Graph (I) Show a very elementary and highly stylized evolutionary process 125 users join our toy OSN over time Become friends with other users over time Become inactive after a while Consider time interval [0, 1], where graph structure changes at time points 1/16, 2/16,..., and 16/16 At any of these discrete points, some friendship relations become inactive, and some new friendships are being established 6/19/20096HotMetrics 2009 - Seattle WA

7. Dynamic Friendship Graph (II) 6/19/2009 t = 1/16 time 7HotMetrics 2009 - Seattle WA

8. Dynamic Friendship Graph (II) 6/19/2009 t = 2/16 time 8HotMetrics 2009 - Seattle WA

9. Dynamic Friendship Graph (II) 6/19/2009 t = 3/16 time 9HotMetrics 2009 - Seattle WA

10. Dynamic Friendship Graph (II) 6/19/2009 t = 4/16 time 10HotMetrics 2009 - Seattle WA

11. Dynamic Friendship Graph (II) 6/19/2009 t = 5/16 time 11HotMetrics 2009 - Seattle WA

12. Dynamic Friendship Graph (II) 6/19/2009 t =6/16 time 12HotMetrics 2009 - Seattle WA

13. Dynamic Friendship Graph (II) 6/19/2009 t = 7/16 time 13HotMetrics 2009 - Seattle WA

14. Dynamic Friendship Graph (II) 6/19/2009 t = 8/16 time 14HotMetrics 2009 - Seattle WA

15. Dynamic Friendship Graph (II) 6/19/2009 t = 9/16 time 15HotMetrics 2009 - Seattle WA

16. Dynamic Friendship Graph (II) 6/19/2009 t = 10/16 time 16HotMetrics 2009 - Seattle WA

17. Dynamic Friendship Graph (II) 6/19/2009 t = 11/16 time 17HotMetrics 2009 - Seattle WA

18. Dynamic Friendship Graph (II) 6/19/2009 t = 12/16 time 18HotMetrics 2009 - Seattle WA

19. Dynamic Friendship Graph (II) 6/19/2009 t = 13/16 time 19HotMetrics 2009 - Seattle WA

20. Dynamic Friendship Graph (II) 6/19/2009 t = 14/16 time 20HotMetrics 2009 - Seattle WA

21. Dynamic Friendship Graph (II) 6/19/2009 t = 15/16 time 21HotMetrics 2009 - Seattle WA

22. Dynamic Friendship Graph (II) 6/19/2009 t = 16/16 time 22HotMetrics 2009 - Seattle WA

23. 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? 6/19/200923HotMetrics 2009 - Seattle WA

24. Measurement - Static Crawling 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] 6/19/200924HotMetrics 2009 - Seattle WA

25. Measurement - Dynamic Goal of sampling: collect a “representative” set of users In 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? 6/19/200925HotMetrics 2009 - Seattle WA

26. Analysis (I) A new approach based on the following two observations in OSNs Clustering at different spatial scales Faster and more noisy temporal dynamics at finer levels of resolutions of the graph Multi-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 MRA DW provides the necessary mathematical framework for performing the above graph coarsening intuition [Maggioni2004] 6/19/200926HotMetrics 2009 - Seattle WA

27. Analysis (II) TOYFB at scale 2 is smaller in size than TOYFB at scale 1 TOYFB at scale 2 has slower dynamics than TOYFB at scale 1 6/19/2009 Scale 1 Scale 2 Scale 3 27HotMetrics 2009 - Seattle WA

28. Analysis (III) 6/19/2009 t = 1/16 time 28HotMetrics 2009 - Seattle WA

29. Analysis (III) 6/19/2009 t = 5/16 time 29HotMetrics 2009 - Seattle WA

30. Analysis (III) 6/19/2009 t = 9/16 time 30HotMetrics 2009 - Seattle WA

31. Analysis (III) 6/19/2009 t = 13/16 time 31HotMetrics 2009 - Seattle WA

32. Conclusion Stop ignoring the dynamic nature of OSNs For 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 advancing OSN 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 6/19/200932HotMetrics 2009 - Seattle WA

33. 6/19/200933HotMetrics 2009 - Seattle WA