It's still a bit of a far cry, but literary scholars are looking for more and more visualization tools to help them compare and contrast large sets of self-similar stories (like the countless variations on the Grail Quest, or the ~350 existing Cinderella stories). One tool I'm trying to develop makes use of braid theory, a subbranch of knot theory, to chart the history of speech-acts between characters -- if strand A passes over strand B, it means character A speaks to character B, and vice versa. The result is often, and expectedly so, messy. But, applied on a single story for all of the speaking characters, it can prove valuable by exposing patterns of speech-acts, moments of conversational dominance (where one thread supersedes all the others), and a number of other visually obvious phenomena that might otherwise have been overlooked. Plays and oral stories prove particularly good subjects. Applied on a slough of stories, a whole data set, especially stories that are supposed to tell the same tale likes the ones mentioned above -- well, it hasn't exactly been done yet; I'm afraid I'm only in my second week of research. But the comparison or juxtaposition may yet prove wonderful and useful, the way knots always have. I suppose the application falls a little more under graph theory than knot theory, but I thought I'd share.

It's still a bit of a far cry, but literary scholars are looking for more and more visualization tools to help them compare and contrast large sets of self-similar stories (like the countless variations on the Grail Quest, or the ~350 existing Cinderella stories). One tool I'm trying to develop makes use of braid theory, a subbranch of knot theory, to chart the history of speech-acts between characters -- if strand A passes over strand B, it means character A speaks to character B, and vice versa. The result is often, and expectedly so, messy. But, applied on a single story for all of the speaking characters, it can prove valuable by exposing patterns of speech-acts, moments of conversational dominance (where one thread supersedes all the others), and a number of other visually obvious phenomena that might otherwise have been overlooked. Plays and oral stories prove particularly good subjects. Applied on a slough of stories, a whole data set, especially stories that are supposed to tell the same tale likes the ones mentioned above, it can prove pretty useful.

Check out the linked TEDx talk for more details: http://www.tedxsmu.org/talks/arnaud-zimmern-braiding-red-riding-hood-tedxsmu-spring-2014/