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6. IMPACT OF RETWEET
We have seen how trending topics rise in popularity and eventually
die in Section 5. Then how exactly does information spread on
Twitter? Retweet is an effective means to relay the information beyond
adjacent neighbors. We dig into the retweet trees constructed
per trending topic and examine key factors that impact the eventual
spread of information.
6.1 Audience Size of Retweet
Figure 14: Average and median numbers of additional recipients
of the tweet via retweeting
People subscribe to mass media in various forms: radio, TV, and
newspapers. They are immediate recipients and consumers of the
news the established media produce. On Twitter people acquire
information not always directly from those they follow, but often
via retweets. Assuming a tweet posted by a user is viewed and
consumed by all of the user’s followers, we count the number of
additional recipients who are not immediate followers of the original
tweet owner. Figure 14 displays its average and median per
tweet against the number of followers of the original tweet user.
The median lies almost always below the average, indicating that
many tweets have a very large number of additional recipients. Up
to about 1; 000 followers, the average number of additional recipients
is not affected by the number of followers of the tweet source.
That is, no matter how many followers a user has, the tweet is likely
to reach a certain number of audience, once the user’s tweet starts
spreading via retweets. This illustrates the power of retweeting.
That is, the mechanism of retweet has given every user the power
to spread information broadly. We recall that influentials by the
number of retweets are dissimilar with those by the number of followers
or PageRank. Individual users have the power to dictate
which information is important and should spread by the form of
retweet, which collectively determines the importance of the original
tweet. In a way we are witnessing the emergence of collective
intelligence.
6.2 Retweet Trees
Knowing that retweet actually delivers information to far more
people than a source’s immediate followers, we are now interested
in how far and deep retweets travel in Twitter. In order to answer
the question we build an information diffusion tree of every tweet
that is retweeted and call it a retweet tree. All retweet trees are
subgraphs of the Twitter network.
We illustrate all the retweet trees of the topic ‘air france flight’ in
Figure 15. In every connected component different colors represent
different tweets. The forest of retweet trees has a large number of
one or two-hop chains. We find interesting retweet patterns such
as repetitive retweet and cross-retweet; the former is repeatedly
retweeting the same tweet, and cross-retweet is retweeting each
other.
In Figure 16 we plot the CCDFs of the retweet tree heights and
the number of users in a retweet tree. The height of 1 is the most
common claiming 95:8%. As 97:6% of node pairs have less than
6 degrees of separation, all retweet trees but for a handful have
a height smaller than 6, and no tree goes beyond 11 hops. The
distribution of the users in a retweet tree follows power-law. This
retweet tree analysis demonstrates how retweets spread and how
many get involved.
6.3 Temporal Analysis of Retweet
We have seen in Section 6.2 that most retweet trees have a height
of one, but retweets reach a good number of people no matter how
many followers the tweet source has. Here we investigate how soon
retweets appear and how long they last. Figure 17 plots the time
lag from a tweet to its retweet. Half of retweeting occurs within an
hour, and 75% under a day. However, about 10% of retweets take
place a month later.

In Figure 18 we plot the time lag between two nodes on a retweet
tree. As most retweet trees are one-hop deep, the time lag on the
first hop is spread out, with the median at just under 1 hour and the
inter-quartile range expanding from a few minutes to more than a
day. What is interesting is from the second hop and on is that the
retweets two hops or more away from the source are much more
responsive and basically occur back to back up to 5 hops away.
Cha et al. reports that favorite photos diffuse in the order of days
in Flickr [4]. The strength of Twitter as a medium for information
diffusion stands out by the speed of retweets.

6.4 Favoritism in Retweet
When a user retweets, the user may or may not retweet evenly
from those whom the user follows. Also from the perspective of
a user who gets retweeted, the retweet may or may not take place
evenly among one’s followers. How even is the information diffusion
in retweet? To answer this question we investigate disparity [2]
in retweet trees.