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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?

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assessing the effects of a soft cut off in the twitter social network

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

NiloyGanguly, SaptarshiGhosh

restrictions in osns
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
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
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 …

empirical measurements on twitter
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]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)
scatter plot of followers following spread1
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
Degree Distributions
  • In-degree distribution: power-law over a large range of in-degrees
degree distributions1
Degree Distributions

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

objectives
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
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
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
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
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
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)

objectives1
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
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
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
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
slide23

Thank You

Contact: niloy@cse.iitkgp.ernet.in

Complex Network Research Group (CNeRG)

CSE, IIT Kharagpur, India

http://cse.iitkgp.ac.in/resgrp/cnerg/