1. Why do people become inactive in Twitter?

We analyze the role of popularity (amount of followers) and reputation (in-coreness) in users becoming inactive in Twitter, and if inactivity in the Strongly Connected Component is lower. Updating a large dataset from 2009 with more than 40 millon Twitter users, we check the date of their last tweet in 2016.

We want to study users that were still active in 2009, but became inactive by 2016. We mark a user as inactive if the date of their last tweet is more than 3 months ago (the blue line). We find that about 35% of the users in the dataset are still active.

Here you see the ratio of inactive users in each of the groups of the bow-tie of Twitter. Users in the Strongly Connected Component are less likely to become inactive than the rest.

To have an idea of the dependence between inactivity and popularity and reputation, we split popularity and reputation in bins and calculated the ratio of inactive users in each bin. You can see that, for low values of popularity and reputation, inactivity goes down, but for some values between 100 and 1000 it goes up. Could it be that sometimes popularity and reputation are demotivating?

We fitted polynomial logistic regression models to predict if users become inactive or not depending on their popularity and reputation. This plot shows what the models predict for the possible values of reputation and popularity. The models confirm what we saw above: in Twitter, not always more popularity and more reputation is more motivating!

2. Which users become more popular in Twitter?

We look at active users in 2016 and study how their popularity has grown since 2009. We test if reputable users and users in the Strongly Connected Component grow more in popularity. First, let’s take a look at the distribution of popularity in 2016:

The logarithm of popularity looks prety much like a normal distribution, which means that popularity is heterogeneous but not as much as a power-law.

How does popularity change between 2009 and 2016? We can get an idea with this 2D histogram:

Seems that users with relatively low popularity grew a lot, but growing was harder for the most popular.

What is the role of reputation in all this? We fitted a model to predict popularity in 2016 as a combination of popularity and reputation in 2009. Here we show the model fit of popularity versus reputation for various values of the previous popularity:

Reputation helps to grow in popularity, but only to those that already were a bit popular, roughly above 100 followers.

We then fitted a model of the growth in popularity for each part of the bow-tie:

Growth in popularity is strongest in the SCC and the Out group, which are the users followed by the SCC. The growth was much lower in the rest, and there was no significant growth in the In group. From this we deduce that being followed by the SCC is necessary for popularity growth.

3. What makes people influential in Twitter?

We measure social influence as the average amount of retweets that each user was getting in 2016. Then we fit a model depending on popularity and reputation. These are the social influence values versus popularity for various values of reputation:

It’s clear that social influence grows sublinearly with popularity: You influence more your 10th follower than your 10000th. Reputation has a negative effect on average, but softens the sublinearity of popularity, which means that as reputation goes up, the relationship between influence and popularity approaches a linear relationship. You can see that in a 3D plot: