We address the online virtual network embedding problem within the Cloud's backbone to optimally map the virtual routers and links in the substrate network in order to maximize the Cloud's provider revenue. Since the problem is NP-hard, we propose a novel approach, named VNE-GH, to significantly reduce the problem size using the Gomory-Hu transformation without losing useful information on the virtual network embedding problem. Starting from the Gomory-Hu compact tree structure, we formulate the virtual network embedding as an Integer Linear Program and resolve the reduced size problem using the branch- and-cut algorithm. Results obtained via extensive simulations show that VNE-GH outperforms the most prominent related work strategies in terms of i) acceptance rate of virtual network requests and ii) Cloud provider's revenue