This paper presents an eigendecomposition approach for virtual resource embedding in cloud infrastructures. Instead of relying on combinatorial or iterative approaches, the method uses structural description of resource graphs to achieve near optimal joint node and link mapping. The solution extends and generalizes prior work on eigendecomposition of the adjacency matrices for undirected graphs to handle weighted graph requests and substrate graphs of different topologies and sizes. The method is compared to an optimal combinatorial solution and a heuristic using topology patterns and a bipartite graph matching that embed simultaneously nodes and links in cloud resources. A matching close to optimal can be found more efficiently by the proposed method as reported in the simulation experiments used for performance evaluation and comparisons. The proposed algorithm exhibits better scalability properties and naturally achieves consolidation that can be tuned according to desired performance tradeoffs