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First, let's get some technical details out of the way. Social networks like Twitter are composed of "nodes", which are individual users, and "edges," which are the ties between them. The number of edges, or ties, connected to a particular node is referred to as that node's degree. In a Twitter network edges have a direction; the tie signifies either that one is following or is followed by another user. The number of edges pointing towards a node - how many others are following that person - is called the indegree.

Accounts that are likely to be bots will tend to have a small indegree. That's because Twitter bots, in general, don't come even close to passing the Turing test; when real people look at them, it is obvious that they are bots. As a result, these fake accounts tend to have 0, or at least very few followers. Based on this, we looked at the proportion of new followers with low follower counts as a proxy for determining the proportion of the accounts that were likely to be "followers for hire." More sophisticated bot networks can use algorithms to follow each other in an attempt to mimic indegree distribution of authentic users. But since our method tests for how distributions differ, it can detect any notable deviation from the expected distribution, not merely the over-presence of accounts with small indegree we would expect from unsophisticated bots.

Our test is based on the underlying assumption that the followers of Twitter accounts tend to display a some kind of general indegree distribution. Exploratory analysis revealed that this distribution varies depending on the size of the original account. We are able to detect probable bot involvement because this distribution would be quite difficult to mimic in a bot network, so presence of many bot followers skews this distribution.

Using TwitterCounter's lists of most followed users, we selected the twenty accounts closest in size to both Romney and Obama, with approximately the same number of followers; ten had slightly fewer followers, ten slightly more. For Romney the twenty accounts were selected from those listed within the Eastern Standard Time-zone. No such restriction was possible for Obama, since his is the 6th most followed account globally, with nearly 18 million followers.

We looked at the indegree distribution of the 150,000 most recent followers from each account in our sample, to see if Romney's dramatic follower spike was truly as suspect as it seemed. This allows us to see the proportion of followers that have very small indegree, and are likely to be bots. On Twitter, degree distributions for networks of a particular size tend to follow a fairly consistent pattern, although this distribution differs notably between very large networks, like Barack Obama's, and medium-size networks, like Mitt Romney's. By comparing the presidential candidates' distributions to the distributions of our set of other accounts of roughly the same size, we were able to see if either Romney's or Obama's new followers differed significantly from the typical distribution.