My first inclination was to just run the full text of The Sun Also Rises through a text analysis program, and see what kind of surprises I found. The result of that initial foray (via Wordle) is here:

What's surprising about this is the complete dominance of the name "Brett"--sure, she's a major character, but she only appears in 11 of the book's 19 chapters, so the fact that her name is so obviously omnipresent in the novel surprised me!

I then ended up playing around with Voyant--a piece of software I can't claim to have fully mastered (as best I can tell it offers up the words most commonly following the key words one gives it in the text)--and charted out a couple of the things going on in the book. The first was to think about a connection between the novel's title and its contents--asking the question of what else, besides the sun, rises in the novel... I looked at the word rise (and "raise," "risen," etc) and a number of its synonyms, to see if any obvious patterns emerged. I have to say that was a fairly unfruitful exercise:

Finally, I used Voyant for a similar visualization of the novel's main characters--an analysis which supports the assertion that the characters' lives are hopelessly interwoven not only socially, but textually as well: