Quantifying Matthew Effect of Twitter

It is well known that most of tweets are retweeted only a few times at most, while very few tweets get a very large number of retweets. This concentration of retweet is caused by a so-called Matthew effect of Twitter; original tweets that have been retweeted more often are more likely to be retweeted further. In this paper, we quantify the Matthew effect of Twitter by using the model, under which the probability that an original tweet (say, tweet A) is retweeted is proportional to a given function $f(i)$, where $i$ denotes the number of retweets that tweet A has received so far. We assume that $f(i)$ is a non-decreasing function of $i$. The proposed model, a simple extension of the Yule process, is analytically tractable and the expression of the distribution of the number of retweets that an original tweet receives can be explicitly obtained. We show that by assuming $f(i)=a+i^{\delta}$ and $\delta$ is around 0.8, the distribution of the number of retweets based on the proposed model is well consistent with the actual distribution.