1. A computer-implemented method implemented in modules of a computer apparatus for discovering a topology of a multitier compute infrastructure, the method comprising: discovering components in the multitier compute infrastructure, including components in an application tier, compute tier, and network tier; discovering physical relationships between components in the multitier compute infrastructure, including components in the application, compute, and network tiers and a containment of applications on hardware components; generating an inventory of discovered components and the physical relationships, including a business services component table indicating business services, an application component table, and a network component table, wherein a business service defines relationship between components in the multitier compute infrastructure and business functions; and deducing non-physical relationships between components in the inventory, based at least in part on information obtained in the operations of discovering components and discovering physical relationships, wherein the deduced non-physical relationships comprise at least one of transactional dependencies indicating connectivity between applications and service dependencies indicating services an application uses, and wherein the deduced non-physical relationships include at least a first relationship table identifying a containment relationship of the network components indicated in the network component table containing application components indicated in the application component table, and a second relationship table identifying business services and the application components indicated in the application component table that perform the business service functions; generating the topology map of the multitier compute infrastructure to include information from the generated inventory and the deduced non-physical relationships.