The graphs are just illustrations. The actual graphs would be high-dimensional (one dimension or axis for each word in the total word set), and each axis would

The graphs are just illustrations. The actual graphs would be high-dimensional (one dimension or axis for each word in the total word set), and each axis would have only two ticks on it: 0 and 1. A post is mapped to the binary vector in this space whose coordinates are determined by the presence or absence of words in the post.