1. A direct connect virtual private interface comprising: a physical port configured to receive one physical connection in order to provide respective virtual connections for multiple virtual private clouds within a public cloud provider infrastructure; and at least one physical hardware router in communication with the public cloud provider infrastructure via the physical port, where the virtual private clouds comprise respective on-demand configurable pools of shared computing resources allocated within the public cloud provider infrastructure that provide a level of isolation via access control mechanisms between respective organizations using the virtual private clouds, where the direct connect virtual private interface is configured with private virtual interfaces to provide, for each virtual private cloud, a virtual connection between the virtual private cloud within the public cloud provider infrastructure and the at least one physical hardware router, and where the at least one physical hardware router comprises respective virtual routers for the virtual private clouds, each virtual router configured to import respective routes for the virtual private clouds from the other virtual routers to enable the virtual private clouds to exchange traffic with one another over the private virtual interfaces via the at least one physical hardware router.