TITLE: Vector bundles on graphs
QUESTION [6 upvotes]: Vector bundles over manifolds have fundamental importance in differential geometry, algebraic topology etc. Are there any applications of this concept (or some variation of it) for graphs (finite or infinite)?
The only place I have seen something like this is in a paper on spanning forests by Kenyon, where the application seems somewhat specialized.

REPLY [3 votes]: Another cool paper is 
http://arxiv.org/abs/1107.5588
Where they talk about line bundles on graphs (and define very nice new class of integrable systems).