The Data-Driven, 21st-Century 'Choose Your Own Adventure'
theatlantic.com
theatlantic.com
Done right branches can be very immersive, increasing the impact of a story dramatically. While legitimate copies are very hard to come by these days, I highly recommend Phantom of Inferno if you are interested in this kind of storytelling.
An alternative use of hyperlinks might be to tell the story from a different character's point of view; books often switch view-point characters. Orson Scott Card exploited his Ender's Game with a whole new book retelling the same events from another character's perspective (Bean).
A difficulty is that changing view-point is often tied up with narrative - e.g. it's used as a way to reveal/hide events as part of a story - which would be undermined if the reader could switch at will. It could be done so as to not affect this, but then the different view-points don't affect the plot; of course, it could add colour and texture, by exploring different perspectives. It's just that you can't use them for sequence: suspense, reveal, resolution, movement.
[or, if you do use them for sequence, you then have to deal with the exponential explosion - and even if you do manage that, it's not necessarily interesting to the reader, except to admire the virtuoso performance.] I don't mean to sound harsh, just thinking aloud.