Assessing the Effects of a Soft Cut-off in the Twitter Social Network

1. Assessing the Effects of a Soft Cut-off in the Twitter Social Network NiloyGanguly, SaptarshiGhosh

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. Reproduced from [Krishnamurthy, WOSN 2008] Scatter plot of followers/following spread • 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.) • Nij(t) : number of nodes having in-degree i, out-degree j at time t • Change in Nij (t) due to change in in-degrees • Change in Nij (t) due to change in out-degrees Details in Networking 2011…

15. Modeling restrictions • βij = 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 • wu: 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 – wu 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 wu ? Values for s,κ chosen by Twitter justified for wu = 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. Thank You Contact: niloy@cse.iitkgp.ernet.in Complex Network Research Group (CNeRG) CSE, IIT Kharagpur, India http://cse.iitkgp.ac.in/resgrp/cnerg/