## 4 Data, Analysis, and Observations
### Exploratory Analysis of Subreddit Data  
We started our experiments with an exploratory analysis of our dataset. We began by creating the subreddit interaction graph (SIG) for the subreddits using data obtained from our crawler. Then we looked at the degree distribution for the subreddits in order to understand the nature of interaction (follower-following) patterns inside them. We also looked at various centrality measures, namely information centrality, degree centrality, and closeness centrality, for these graphs. Centrality measures induce a ranking on the nodes of the underlying graph based on their position in the social network. They can be used to identify, for example, the most influential nodes in the social network. Though we did not use centrality measures for our algorithms, they provide an initial overview of the structure of the subreddits in terms of the user interactions and central nodes. Figures 12 and 13 show the information centrality for the graphs of subreddits _Acoustic Neuroma_ and _Adventure Builders_ respectively. Note that the nodes in these graphs are color coded with \"red\" being the nodes with the highest centrality values and \"green\" being the ones with the lowest. Furthermore, the edges in the graphs capture the \"reply\" relationship. Thus, if there is an edge from node \"A\" to node \"B\", it means that \"A\" replied to a post by \"B\". It should be clear from the graphs that the nodes with the highest centrality values are either followers (those who respond) or leaders (those who post) and hence the centrality values do not help to identify one group over the other. Figure 12: Information centrality sorted by node color for subreddit “Acoustic Neuroma”. Note that the color red and its shades signify high centrality value, whereas the color green and its shades signify smaller centrality values. Next, we considered the degree distribution. Since the graphs are directed, each node has an in-degree and out-degree. In general, one expects that the degree distribution will have a power law structure where a lot of users (nodes) will have small degrees, whereas a few nodes will have a large degree. In our first attempt at generating the degree distributions for each subreddit, we used a = 4, b = 20 for pruning. The degree distributions obtained from the pruned SIGs did not have the power law structure. Looking into this further, we realized that most of the degree distributions had one node with a significantly higher degree than the others in the subreddit. Hence, while trying to visualize the degree distributions with this specific node included, the other nodes were being lumped into a compressed plot which was camouflaging the power law structure of the distribution. Looking into this further, we realized that the node with a significantly higher degree than the others was not a real user but a dummy node called \"deleted\". Upon further analysis, we found that this was a specific artifact introduced by the implementation of Reddit's \"delete account\" functionality. When a user deletes their account, they are removed from every subreddit in which they were members. However, this is implemented in Reddit by creating a single node in each subreddit called \"deleted\". When a user account is removed from a subreddit, the user is \"merged\" into this dummy user called \"deleted\" and all interactions of the user are marked as being from this \"deleted\" node. Thus, if there are two unique users, \(u\) and \(v\), and they delete their accounts, then both the users are merged into the node \"deleted\" and the totality of their interactions are now shown to be from this deleted node. If anyone analyzes the interaction pattern of the subreddit at this point in time and creates implicit relationships based on these interactions, the \"deleted\" node will have a degree equal to the sum of the degrees of \(u\) and \(v\) (and other deleted users if there are any).