1. A method of migrating applications from an enterprise-based network to a multi-tenant network of a compute service provider, the method comprising: receiving a request to migrate an application running on a first virtual machine instance within the enterprise-based network, wherein the request is received in a migration service of the compute service provider; determining dependencies of the application by identifying at least a second virtual machine instance within the enterprise-based network, wherein the at least second virtual machine instance is associated with the application; receiving resource monitoring metrics associated with hardware resources used by the first virtual machine instance and the at least second virtual machine instance, wherein the hardware resources are associated with at least one host server computer hosting the first virtual machine instance and the at least second virtual machine instance; selecting, based on the resource monitoring metrics, a virtual machine instance type from a plurality of available virtual machine instance types at the multi-tenant network of the compute service provider for each of, at least, the first virtual machine instance and the at least second virtual machine instance; migrating the first virtual machine instance and the at least second virtual machine instance from the enterprise-based network to each of the selected virtual machine instance types, wherein the selected virtual machine instance types are hosted by a server computer within the multi-tenant network of the compute service provider, thereby migrating the application from the enterprise-based network to the multi-tenant network of the compute service provider; and configuring a network topology within the multi-tenant network of the compute service provider in which a physical, hardware-based connection topology of the enterprise-based network is at least partially emulated on the multi-tenant network of the compute service provider by the server computer within the multi-tenant network of the compute service provider, wherein configuring the network topology is controlled through client input to the migration service of the compute service provider, and wherein at least a partial network configuration of the physical, hardware-based connection topology of the enterprise-based network is preserved upon migration of the application to the multi-tenant network of the compute service provider, including preserving an internet protocol address and a host name of an enterprise-based server or preserving a virtual machine server dependency of an enterprise-based network application.