A network-configuring system creates stable virtual interfaces for groups of neighboring network nodes. During operation, the system can obtain network-neighborhood information from one or more network neighbors. This network-neighborhood information includes duplex-neighborhood information that indicates at least a set of neighboring devices to the network neighbor, and a set of remote network nodes which are accessible via a respective neighbor. The system can use the network-neighborhood information to determine one or more groups of network neighbors with common network characteristics, such that a respective group includes one or more mutually-connected network peers. The system can then define a virtual interface for a respective group of stable network neighbors, such that the virtual interface's member nodes include the local network node and the respective group's mutually-connected network peers.