This document summarizes a study that analyzed meme diffusion on Twitter and developed an agent-based model to simulate meme competition for limited user attention. The study collected Twitter retweet data, analyzed statistical properties of meme diffusion networks and user behavior, and found that users' limited attention and social network structure were sufficient to reproduce the observed patterns. The model demonstrated that strong or weak user attention failed to match real-world data, indicating attention level affects meme popularity distributions.

1. DIE
Jul.24, 2013
Kazutoshi Sasahara
Featured Article:
Competition among memes in a world of limited attention
L.Weng, A. Flammini,A.Vespignani, and F. Menczer, Scientific Reports (2012)
doi:10.1038/srep00335

2. • Summary
• Introduction
• Twitter Data Analysis
• Agent-based Simulation
• Discussion

3. Summary
• Question
How our limited attention affect meme diffusion in online world?
• Approach
- Data analysis for statistical properties of meme (hashtag) diffusion
- Agent-based model to capture these properties
• Result
Without exogenous factors, the proposed model (limited attention
+ social network structure) can account for the observed
statistically properties of memes and users.

4. • Summary
• Introduction
• Twitter Data Analysis
• Agent-based Simulation
• Discussion

5. Introduction (1/2)
• The advent of social media has lowered the cost of information
production and broadcasting, boosting the potential reach of ideas
or memes.
• However, the abundance of information is exceeding our cognitive
limit (cf. Dumber’s number).
• As a result, memes must compete for our limited attention.
(cf. economy of attention).

6. Introduction (2/2)
• Social data allows us to quantify meme diffusion; yet it is hard to
disentangle the effects of limited attention from other factors:
- social network structure
- the activity of users
- the size of audience
- the different degrees of influence of meme spreaders
- the quality of memes
- the persistence of topics,
...
• The authors explicitly model mechanisms of competition among
memes, exploring how they drive meme diffusion.

7. • Summary
• Introduction
• Twitter Data Analysis
• Agent-based Simulation
• Discussion

8. Data Collection and Use
• Collection of retweets
• 2010.10 ~2011.1
• 120M retweets and 1.3M hashtags from 12.5M users
* The user network shows a scale-free degree distribution.
• Sampled user network
• Users are sampled by a random walk sampling method
• 105 nodes, 3×106 links
• Parameters for posting (pu, pr, pm) and time window (tw)
are estimated from the empirical data for modeling

9. Data Analysis (1/4)
Meme Diffusion Networks
Nodes:Twitter users
Links: Retweets that carry the meme (i.e., hashtag)
Memes about the
Japan earthquake
Political memes
related to the US
republican party
Arab Spring

10. Data Analysis (2/4)
Limited Attention
S =
X
i
f(i) log f(i)
f(i): the proportion of tweets
about meme (hashtag) i
The breadth of attention of a user
~ Shannon entropy
A user’s breadth of attention remains constant irrespective of system diversity.
→ The diversity of memes to which a user can pay attention is limited.

11. Data Analysis (3/4)
User’s Interests and Memory
sim(M, I) =
2 log[minx2MIf(x)]
log[minx2M f(x)] + log[minx2If(x)]
Maximum information path similarity
considers shared memes but discounts the more
common ones (Markins and Menczer 2009).
User’s interest (Iu):
The set of all memes that a user (u) has retweeted
in the past
User’s memory (Mn):
The n most recent memes across all users
(M0 :The set of new memes)
f(x) :The proportion of a meme (x)
Users are more likely to retweet memes about which they posted in the
past (ρ=0.98). → Memory is important for meme diffusion.

12. Data Analysis (4/4)
Empirical Regularities
a, b, c:
Long-tailed
distributions across
different time-scales
(=1-CDF)
(=1-CDF)
d: Peaked but wide distribution
Some users have broad attention while
others are very focused.
Weekly measured

13. • Summary
• Introduction
• Twitter Data Analysis
• Agent-based Simulation
• Discussion

14. Model Description (1/3)
Meme Diffusion Model
• Memes ~ hashtags
• Twitter user ~ Agent with a screen and a memory (finite
size)
• Twitter user network ~ A frozen network of agents
• Nodes :Agents
• Links : Friend-follower relationships
e.g.,A→B (= B follows A)
• The network structure is determined based on a subset of
the empirical data (# of nodes = 105)

15. Model Description (2/3)
Parameters (estimated from the data)
• Tweet behaviors
• Pn : Probability of posting a new meme
0.45 ± 0.5
• Pr : Probability of retweeting a meme in the screen
Standard(0.016), ER(0.029), weak(0.205), strong(0.001)
• Pm : Probability of posting a meme in the memory
0.4 ± 0.01
• Time window (tw)
in which memes are retained in an agent’s screen or memory
• tw < 0 : Less attention Strong competition
• tw = 0 : Standard
• tw > 0 : More attention Weak competition

16. A
B
C
D
E
F
A’s friends = {B, C, D}
A’s followers = {E, F}
Received memesPosted memes
Model Description (3/3)
Illustration of the Model
Post a new meme
(Pn)
RT a meme
(1- Pn):
1) from screen (Pr)
or
2) from memory
(Pm)

17. Simulation Results (1/2)
Effects of Social Network Structure
The observed quantities is greatly reduced when memes spread on a random network.
tw= 1 (standard)The model captures the key features of the empirical data.

18. Simulation Results (2/2)
Effects of Limited Attention
Strong attention fails to reproduce the meme lifetime distribution (a).
(strong)
(weak)
Weak attention fails to generate extremely popular memes nor extremely active users
(b, c).

19. • Summary
• Introduction
• Twitter Data Analysis
• Agent-based Simulation
• Discussion

20. Discussion (1/2)
• The model demonstrates that a combination of
limited user attention and social network structure
is a sufficient condition for the observed statistical properties of
memes and users:
• Long-tailed distributions of meme lifetime and popularity, and user activity
• The breadth of user attention
• At the statistical level, exogenous factors are not necessary:
e.g., meme’s quality, user’s personality, external events
Source of
heterogeneity
meme
competition

21. Discussion (2/2)
• Related Studies
• The decay in news popularity ~ a multiplicative process with a
novelty factor (Wu and Huberman 2007)
• Bursts of attention toward a video ~ an epidemic spreading
process with a forgetting process (Crane and Sornette 2008)
None of them explicitly modeled meme competition
• The economy of attention has always been assumed implicitly and
never tested.This is the first attempt to explicitly model
mechanism of competition.