The size of a subreddit is set by how often the others talk about it in sum. One connection represents the mutual mentions of the two linked communities. The widths on each end of it is determined by the relative frequency of the (adjacent) mentionee being referenced by the respective (distant) mentioner. The color of a connection comes from the subreddit mentioned more often by the other one of this connection.
If you move your mouse over the annulus sector of one subreddit, you get the information regarding that one in an isolated view. This way you can see more clearly how in our example here A is mentioned very often by C, but A itself mentions C only rarely.