1. Competition among memes in a
world with limited attention
Complex Systems - L.M. Informatica - A.A. 2014/2015
Andrea Sghedoni - MATR. 0000736038

2. Summary
❏ Introduction
❏ Twitter
❏ Limited Attention
❏ User interests
❏ Empirical Results
❏ Memes Lifetime - Meme popularity Charts
❏ Simulation Results
❏ Model description
❏ Simulation config
❏ Simulation 1 - Social Network Structure
❏ Simulation 2 - Limited Attention
❏ Conclusions
❏ Bibliography

3. Introduction
● In the context of social network, every user is able to produce and transmit
information
● The wide adoption of social network has increase the competition among
memes/ideas for our limited attention
● Our limited capacity can not consume all information that spread in a social
network
● The social networks are opportunities to study the user behavior and
competition among different memes in process diffusion
● Few memes can become very popular thanks to social network structure
and competition

4. Twitter
● Empirical results from Twitter microblogging
● Main concepts:
○ follower/following → link among users
○ tweet → personal user post - 140 char
○ retweet → it carries a meme from user to user
○ hashtag → #keyword, it brings an idea

5. Limited attention
● The breadth of attention of a user
○ Shannon entropy S = - ∑i
f(i) log f(i)
○ f(i) → portion of tweets about meme i
● N tweets, user Shannon Entropy :
○ S → 0, all tweets are about the same meme
○ S → log n, all tweets are about n different
memes
● The chart shows how user entropy is quite the
same for all time considered, while system entropy
increase its value [proof of limited attention of
users]
Measurement day

6. User interests
● Interests + present & past behavior → future
behavior
● Iu
→ user interests
● M1,..,n
→ set of n potential candidates for a
retweet
● Sim(M1
,Iu
), ...,Sim(Mn
,Iu
) → Similarity between
the user interests and the actual and
candidate posts
● P(retweet(u,M) | Sim(M,Iu
)) → Probability that
an user u retweets a posts in M, given the
similarity between M and Iu

7. Empirical results
● Dataset :
○ Oct 2010 - Jan 2011
○ 12,5 millions users
○ 1,3 millions hashtags
○ 120 millions rt
● MEME LIFETIME → maximum number of consecutive time
units in which posts about the meme are observed
● MEME POPULARITY → number of users per day who tweet
about a meme, measured over a given time period

8. Meme lifetime and Meme Popularity
● Power Law f(x) = cx-α
● Extremly heterogeneous behaviors
● Some memes are very popular and persistent, but all the others die quickly

9. Model description
● Each user can generate, with uniform probability, new post or
retweet one and mantains a time-ordered list of posts
● Screen (received memes) and Memory (posted memes) → finite
capacity
● Top of the list → Recent tweets and retweets
● Memory mechanism → history is important for the future user
behavior
● Modelling of limited attention → posts survive at agent’s list for a
finite amount of time
● Large number of posts about same meme → it survives for a long
amount of time and can be forwarded in the social network

10. Simulation config
● Direct graph with 105
nodes (users) and 3x106
edges → empirical data
subset
● Simulation 1 - Social Network structure
○ Study of structure network in the meme diffusion process
○ Behavior of model on Random Graph (Erdӧs-Rényi ER)
● Simulation 2 - Limited attention
○ Study of limited user attention in the meme diffusion process
○ tw
→ time window in which a particolar post is manteined in agent’s
screen or memory
○ tw
<1 → less attention, more competition
○ tw
>1 → more attention, less competition

11. Simulation 1 - Social Network Structure
● ER → heterogeneity is very reduced
● ER degree distribution is narrow (Poisson distribution)
● Real Social Network → Havy tailed distribution
● ER Network has no hub users

12. Simulation 2 - Limited attention
● tw
= 0.1 (high competition)→ Lifetime very short, High popularity
● tw
= 5 (low competition)→ Very low popularity
● tw
= 1(standard model)→ Near to empirical data

13. Conclusion
● Social network structure + Competition for user limited
attention → sufficient condition for large heterogeneity in
meme popularity and lifetime
● No assumation about meme appeal, user influence, external
events
● Ecosistem Similarity
○ individuals → posts
○ different species → memes
○ environment with limited number of individuals → user
limited attention

14. Bibliography
● L. Weng, A. Flammini, A. Vespignani, F.Menczer
“Competition among memes in a world with
limited attention”, Indiana University, 29/03/2012