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Assessing the Effects of a Soft Cut-off in the Twitter Social Network
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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: [email protected] Network Research Group (CNeRG) CSE, IIT Kharagpur, Indiahttp://cse.iitkgp.ac.in/resgrp/cnerg/
Thank You