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

Niloy Ganguly, Saptarshi Ghosh

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

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

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 …

Does the Twitter follow-limit really affect many users?

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

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)

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

Degree Distributions

In-degree distribution: power-law over a large range of in-degrees

Degree Distributions

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

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

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

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…

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 …

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

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)

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

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 …

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

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

Thank you

Contact: niloy@cse.iitkgp.ernet.inComplex Network Research Group (CNeRG) CSE, IIT Kharagpur, Indiahttp://cse.iitkgp.ac.in/resgrp/cnerg/

Thank You