I've read (and I've been told in lectures) that each graph (let's just say a combinatorial graph) corresponds to a topological space called the geometric realization - in this space the vertices are distinct points and the edges are subspaces homeomorphic to [0,1]. My question is this: Is this provable? I mean, lots of book say this but I'm not entirely convinced. This is probably easy to prove but I have not seen it anywhere. If someone could show me, or instruct me, or provide a link, or something, I would be very happy!