1. Assessing the Effects of a Soft Cut-off in the Twitter Social Network Niloy Ganguly, Saptarshi Ghosh

2. Restrictions in OSNs Restrictions on the number of social links that a user can have  Hard cut-offs: 1000 in Orkut, 5000 in Facebook  Soft cut-off in Twitter Why restrictions?  Scalability issues: reduce strain on OSN infrastructure due to user-to-all-friends communication  Prevent indiscriminate linking by spammers

3. Need to study restrictions in OSNs Conjecture  Restrictions only affect spammers and very few hyper-active legitimate users Reality in today’s OSNs  Thousands of legitimate users are getting blocked  Restrictions being increasingly criticized by socially active and popular users Twitter imposed a soft cut-off that adapts to requirements of popular users

5. The soft cut-off in Twitter u → v: user u ‘follows’ user v Conjectured Twitter follow- limit (“10% rule” ): Restriction on out-degree based on in-degree Need at least 1820 followers to follow more than 2000 Soft cut-off: Can follow up to 110% of number of followers Details in WOSN 2010, Computer Communication 2012 …

6. Does the Twitter follow-limit really affect many users?

7. Empirical measurements on Twitter Several measurements before restriction was imposed (in August 2008) Publicly available crawl of entire Twitter network as in July 2009  41.7 million nodes  1.47 billion social links

8. Scatter plot of followers/following spread Reproduced from [Krishnamurthy, WOSN 2008] In Jan-Feb 2008, before restriction imposed (x, y) implies a user following x (out-degree) y followers (in-degree)

9. Scatter plot of followers/following spread Reproduced from [Krishnamurthy, WOSN 2008] In Jan-Feb 2008, before restriction imposed In Oct-Nov 2009, a year after restriction imposed

10. Degree Distributions In-degree distribution: power-law over a large range of in- degrees

11. Degree Distributions Out-degree distribution (right): sharp spike around out- degree 2000 due to blocked users

12. Objectives Develop an analytical model to predict effects of restrictions  Fraction of users likely to get blocked  Effects of varying linking dynamics Design restrictions balancing the two conflicting objectives  Desired reduction in system-load due to communication  Minimize dissatisfaction among blocked users

13. Directed Network growth model Model by [Krapivsky et. al., PRL 86(23), 2001] extended by incorporating restrictions Growth event 1 (with probability p)  new user u joins and ‘follows’ existing user v  v chosen preferentially on in-degree (popularity) Growth event 2 (with probability 1-p)  existing user u ‘follows’ another existing user v  u chosen preferentially on out-degree (social activity), v on in-degree

14. Growth model (contd.) N ij (t) : number of nodes having in-degree i, out-degree j at time t Change in N ij (t) due to change in in-degrees Change in N ij (t) due to change in out-degrees Details in Networking 2011…

15. Modeling restrictions β ij = 1 if users having in-degree i allowed to have out-degree j, 0 otherwise For a κ % Twitter follow-limit at out-degree s (κ = 10, s = 2000 in reality ) Model solved to derive closed-form expressions for degree distributions in presence of restrictions Details in Networking 2011 …

16. Predictions by the model Accurately matches degree distributions of Twitter OSN Explains decrease in power-law exponent of out-degree distribution in Twitter after imposing restriction

17. Predictions by the model (contd.) Fraction of users who are likely to get blocked  Varies inversely proportional to network density  Reduces rapidly as link-formation becomes more random (as opposed to preferential)  Power-law decrease with starting point of cut-off s  Parabolic increase with κ (κ % (1 + κ -1 ) rule in Twitter)

18. Objectives Develop an analytical model to predict effects of restrictions  Fraction of users likely to get blocked Design restrictions balancing the two conflicting objectives  Desired reduction in system-load due to communication  Minimize dissatisfaction among blocked users

19. Using model to design restrictions Utility function for restrictions  L : reduction in links (communication-overhead)  B : fraction of users blocked / dissatisfied  w u : importance of minimizing user-dissatisfaction (value decided by system engineers) Optimizing U helps fix values of parameters in the restriction function to balance both objectives U = L – w u B Details in ComCom 2012 …

20. Using model to design restrictions (contd.) What values of restriction parameters s, κ will maximize achieved utility U, for given w u ? Values for s,κ chosen by Twitter justified for w u = 50

21. Summary till now … First study of restrictions in OSNs  First attempt to theoretically model effects of soft cut-offs on network growth Soft cut-offs likely to be favored in OSNs over hard cut-offs  Can be applied in undirected OSNs (e.g. Facebook) by distinguishing initiator and acceptor of social links

22. Thank you

23. Contact: niloy@cse.iitkgp.ernet.in Complex Network Research Group (CNeRG) CSE, IIT Kharagpur, India http://cse.iitkgp.ac.in/resgrp/cnerg/ Thank You