1. A system, comprising: a provider network comprising: a plurality of computing devices configured to implement a plurality of resources of the provider network, wherein a set of the plurality of resources of the provider network are allocated to a client of the provider network as a resource collection; and a plurality of endpoint routers configured to provide a link from a respective one of the plurality of endpoint routers to the resource collection via a private connection over the provider network; and one or more computing devices configured to implement a connectivity coordinator, wherein the connectivity coordinator is configured to: implement an interface defining connectivity operations available to the client; receive a connectivity request indicating a logically isolated network connection is desired to be established between a client network of the client and the resource collection of the provider network allocated to the client, wherein the request specifies a dedicated physical path from the client network to a particular endpoint router of the plurality of endpoint routers of the provider network that is to be used to establish the logically isolated network connection; and initiate one or more configuration operations to allow traffic to flow from the client network to the resource collection in accordance with the request.