The main resource allocation research challenge in network virtualization is the Virtual Network Embedding (VNE) Problem. It consists of two stages, usually performed separately: node mapping and link mapping. A new mathematical multi-constraint routing framework for linear and non-linear metrics called "paths algebra" has already been proposed to solve the second stage, providing good results thanks to its flexibility. Unlike existing approaches, paths algebra is able to include any kind of network parameters (linear and non-linear) to solve VNE in reasonable runtime. While paths algebra had only been used to solve one stage (link mapping) of the VNE, this paper suggests an improvement to solve VNE using the paths algebra-based strategy by coordinating, in a single stage, the mapping of nodes and links based on a ranking made of the bi-directional pair of nodes of the substrate network, ordered by their available resources. Simulation results show that the New Paths Algebra-based strategy shows significant performance improvements when compared against the uncoordinated paths Algebra-based link mapping approach.