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Cybersecurity

Analysing the Twitter social graph: Whom can we trust?

Profile image of Evgeny MorozovEvgeny Morozov

2014

Figures (18)
Figure 2: Verified users are followed by more people than they follow. “Followings” are users whom verified users follow. “Followers” are users who follow verified users. The boxplot (outliers are not shown) shows that verified users tend to follow restrictively although they have a large number of followers. This is also shown by the median and maximum values of the number of followings and the number followers of verified users. Therefore, verified users follow selectively, thereby unintentionally providing a checkpoint on the trust of other users in the Twitter graph.
Figure 2: Verified users are followed by more people than they follow. “Followings” are users whom verified users follow. “Followers” are users who follow verified users. The boxplot (outliers are not shown) shows that verified users tend to follow restrictively although they have a large number of followers. This is also shown by the median and maximum values of the number of followings and the number followers of verified users. Therefore, verified users follow selectively, thereby unintentionally providing a checkpoint on the trust of other users in the Twitter graph.
The number of users of each degree (in the 2009 data set) is shown in the Figure 4.
The number of users of each degree (in the 2009 data set) is shown in the Figure 4.
Figure 5: Average total followers per user by degree of trust (log scale)
Figure 5: Average total followers per user by degree of trust (log scale)
Figure 6: Ratio R; of the number of verified followers to the total number of followers for all users by category: verified users, users of trust degree 1, experts, and other users
Figure 6: Ratio R; of the number of verified followers to the total number of followers for all users by category: verified users, users of trust degree 1, experts, and other users
We then plotted the CDF of R2 for all users by category given in Figure 7. R2 upholds the notion of trust as verified users have a higher value than experts. But the problem with this ratio was that being a ratio, the value of R2 was always less than | and it was difficult to find the different trust levels since R> was a continuous metric. We would rather prefer to have a discrete metric.
We then plotted the CDF of R2 for all users by category given in Figure 7. R2 upholds the notion of trust as verified users have a higher value than experts. But the problem with this ratio was that being a ratio, the value of R2 was always less than | and it was difficult to find the different trust levels since R> was a continuous metric. We would rather prefer to have a discrete metric.
Figure 8: Number of verified followers for unverified users. X-axis is in log scale.
Figure 8: Number of verified followers for unverified users. X-axis is in log scale.
The goal was to inspect the trust metrics (mentioned in the previous section) on the 2012 dataset but because of its huge size, we did not work on it until we were sure what method we wanted to apply. After we deduced that the trust score is the best metric for measuring trust, we applied it on the 2012 dataset. But the raw graph (adjacency list) was too huge and required some data processing for making it efficiently accessible by our algorithms. The 2012 dataset has verified users, experts and other users like the 2009 dataset (all distinct
The goal was to inspect the trust metrics (mentioned in the previous section) on the 2012 dataset but because of its huge size, we did not work on it until we were sure what method we wanted to apply. After we deduced that the trust score is the best metric for measuring trust, we applied it on the 2012 dataset. But the raw graph (adjacency list) was too huge and required some data processing for making it efficiently accessible by our algorithms. The 2012 dataset has verified users, experts and other users like the 2009 dataset (all distinct
| Results: The trusted category of users Now that we have seen that the trust score takes distinct values from 0 to 400, the nex question is how to draw the line between who can be trusted and who can’t. We know thé the higher the trust score, the more trusted the person. But we still cannot categorise user into the fourth category of users (trusted users) explained in section 2.1. Above whe threshold value of the score do we classify users to be “trusted”? This is a subjectiv question, and we try to answer that, by first showing how the number of unverified truste users’ varies with increasing threshold values (Figure 11) and then analysing the number o rusted users at some selected threshold levels. Because of the subjective nature of th question, there is no definite answer. Now that we have seen that the trust score takes distinct values from 0 to 400, the next
| Results: The trusted category of users Now that we have seen that the trust score takes distinct values from 0 to 400, the nex question is how to draw the line between who can be trusted and who can’t. We know thé the higher the trust score, the more trusted the person. But we still cannot categorise user into the fourth category of users (trusted users) explained in section 2.1. Above whe threshold value of the score do we classify users to be “trusted”? This is a subjectiv question, and we try to answer that, by first showing how the number of unverified truste users’ varies with increasing threshold values (Figure 11) and then analysing the number o rusted users at some selected threshold levels. Because of the subjective nature of th question, there is no definite answer. Now that we have seen that the trust score takes distinct values from 0 to 400, the next
1.1 The new population We have now seen how the threshold is used to divide the set of unverified users into trusted and not trusted users. But as shown in Figure 1, the interesting subset of users is the trusted set of users in the “other” category (defined in Section 2.1) of users. The trusted users in the “other” category are neither verified, nor are they experts, but are trusted by our method.
1.1 The new population We have now seen how the threshold is used to divide the set of unverified users into trusted and not trusted users. But as shown in Figure 1, the interesting subset of users is the trusted set of users in the “other” category (defined in Section 2.1) of users. The trusted users in the “other” category are neither verified, nor are they experts, but are trusted by our method.
We have taken four sample threshold values to analyse the most optimal threshold value for trust. In the table that follows, we see that there are more than 8.2 million trusted users with a threshold of 2, which means that this threshold is not very stringent, and therefore is not the best choice. We see that more than 600 thousand users are trusted at a threshold of 10, and this seems to be a good value because it makes 0.132% of the users trusted, as compared to the 0.006% verified users. This threshold level is neither too restrictive nor stringent. If we take the threshold of 53, we obtain 29 thousand trusted users, which is almost equal to the 28.8 thousand verified users.
We have taken four sample threshold values to analyse the most optimal threshold value for trust. In the table that follows, we see that there are more than 8.2 million trusted users with a threshold of 2, which means that this threshold is not very stringent, and therefore is not the best choice. We see that more than 600 thousand users are trusted at a threshold of 10, and this seems to be a good value because it makes 0.132% of the users trusted, as compared to the 0.006% verified users. This threshold level is neither too restrictive nor stringent. If we take the threshold of 53, we obtain 29 thousand trusted users, which is almost equal to the 28.8 thousand verified users.
before. In this section we show how the size of this population changes with the threshold. The percentage of trusted users in the “other” category drops significantly as the threshold is increased. And this shows that experts are more trusted, which is why they are called influential as well. But at the threshold of 5, there are 1.1 million trusted users from the “other” category, which is quite a significant amount considering that there are 2.8 million expert users and only 28,819 verified users. The number of trusted users from the “other” category is more than one-third of the experts’ category in size. Thus we have achieved our goal of finding a new population of significant size of trusted users on Twitter.
before. In this section we show how the size of this population changes with the threshold. The percentage of trusted users in the “other” category drops significantly as the threshold is increased. And this shows that experts are more trusted, which is why they are called influential as well. But at the threshold of 5, there are 1.1 million trusted users from the “other” category, which is quite a significant amount considering that there are 2.8 million expert users and only 28,819 verified users. The number of trusted users from the “other” category is more than one-third of the experts’ category in size. Thus we have achieved our goal of finding a new population of significant size of trusted users on Twitter.
Figure 12: The number of users in each score value from 0 to 400 by user category. The verified users and the experts have a similar curve — long tail (which almost merges in the end) and slower decay than other users. This shows that, according to the trust score, experts are more like verified users than other users.
Figure 12: The number of users in each score value from 0 to 400 by user category. The verified users and the experts have a similar curve — long tail (which almost merges in the end) and slower decay than other users. This shows that, according to the trust score, experts are more like verified users than other users.
Figure 13: Although there are much more “other” users, at any threshold level above 6, there are more trusted experts than other users, and this shows that the score upholds the property of experts being influential and having ¢ large impact on Twitter, and therefore are more trusted. Please note that verified users are not shown in this plot.
Figure 13: Although there are much more “other” users, at any threshold level above 6, there are more trusted experts than other users, and this shows that the score upholds the property of experts being influential and having ¢ large impact on Twitter, and therefore are more trusted. Please note that verified users are not shown in this plot.
Figure 14: Scatter plot of the trust score vs the total number of followers of all users. There is no correlation, which means that the trust score cannot be predicted using the number of followers of a user. The red line shows the maximum score that a user with a given number of followers can have.
Figure 14: Scatter plot of the trust score vs the total number of followers of all users. There is no correlation, which means that the trust score cannot be predicted using the number of followers of a user. The red line shows the maximum score that a user with a given number of followers can have.

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References (10)

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