One of the main challenges of network virtualization is the virtual network embedding problem(VNE). The objective of the VNE is to map a set of Virtual Network Request (VNR) to a physical node and link. VNR is composed by a set of virtual nodes and links with several demands (Processing power, Bandwidth.), which they need to be assigned into a set of paths in the substrate network with sufficient resources to accomplish their demands. Furthermore, these embedding can be optimized with regard to several parameters, such as: embedding cost, link bandwidth, energy- efficiency, packet loss rate, throughput, etc. To solve the VNE program a mathematical tools was proposed, called “Paths algebra”. This framework can helped solve the multiple multi- constraint routing problems of VNE using linear metrics as bandwidth, number of hops and delay, or non-linear metrics as availability and package loss rate Most of the existing VNE proposals treat the single-path virtual link-mapping problem as a mono-constraint, that is, their objective is to map the virtual links in substrate paths that minimize/maximize the usage of one resource (typically bandwidth). This paper introduces a virtual link mapping approach supporting multiple constraints using the “paths algebra” routing framework