## 4 Data, Analysis, and Observations
### Analysis of Interconnectedness of Subreddits
An example a leader-follower interaction for a NSFW subreddit is shown in Figure 18. From the structure of this graph, we can conclude that the users of this subreddit (after pruning the less active users) are associated with one or more leaders implicitly through their responses to the leader's posts (see Section 3 for details on identifying implicit leaders). This in turn establishes that the leaders drive the conversations in a subreddit through their posts whereas the followers consume the information being driven by the leaders. To see this more objectively, we defined a \"leaderness score\" or each implicit leader in a subreddit. It is defined as the ratio of the total number of unique users who have responded to a leader to the total number of users in a subreddit. Intuitively, this score shows the importance of a leader: the higher the score, the more the following of the leader, and the greater their influence. We studied the \"leaderness score\" for the implicit leaders of the top five highly interconnected subreddits. The result for one of the subreddits is shown (named \"b_cups\") in Table 1. Note that this is the first highly interconnected subreddit. The table shows the top five implicit leaders in the subreddit and their associated \"leaderness score\". Note that this subreddit has a total of 3322 users, and hence, we can conclude that approximately 1% of the users follow some implicit leaders. Note that out of these 3322 users, after pruning, we were left with only 429 active users which were used to compute the \"leaderness score\". Hence, one can clearly see that a significant fraction of the active users followed one of the top five implicit leaders. This establishes the fact that the leaders drive the conversations in the highly interconnected subreddits. \begin{table}
\begin{tabular}{c c} \hline \hline
**User ID** & **Leaderness Score** \\ \hline
2295 & 0.01384708 \\
2258 & 0.01384708 \\
2455 & 0.012040939 \\
410 & 0.011137869 \\
2360 & 0.010234798 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Leaderness score for implicit leaders in NSFW subreddit “b_cups”. Figure 14: Reddit Interconnectedness Graph (RIG) for subreddits. This figure shows the interconnections of the top 250 interconnected subreddits. The nodes are color coded by the interconnectedness score: 0.003 vivid blue, 0.002571 laps lazuli, 0.002142 deep sky blue, 0.001714 medium sea green, 0.001285 olive drab, 0.000857 olive green, 0.000428 bronze, and less than 0.000428 dark red. Note that the highly interconnected subreddits are shown in shades of blue and are clearly discernible as two groups of nodes arranged in circles. Note that there are three such groups which are shown in black circles. The largest is arranged in the form of a large circle on the right and the other two groups are on the bottom and left, respectively. The subreddits in these groups are highly interconnected among themselves and they are sparsely connected with other non-NSFW subreddits (see Figure 15). Note that the names of the subreddits in these groups establish that they are NSFW, and we have also verified the same manually. Figure 16: Smaller groups of interconnected subreddits as seen in Figure 14. **(a)** Smaller group of five interconnected NSFW subreddits. **(b)** Smaller group of seven interconnected NSFW subreddits. Figure 15: This figure shows the sparsity of interconnections between the NSFW and non-NSFW subreddits. Note that as we have pointed out in Figure 14, the large group pf blue nodes are all highly interconnected and NSFW. However, as seen in this figure, the interconnections between the nodes in the NSFW group and their non-NSFW neighbors are sparse, indicating the lack of interactions between these groups. It must be noted that there are many non-NSFW subreddits in the neighborhood as seen here, but they do not interact with the NSFW ones.