The disclosed embodiments provide a system that automatically detects a role of a node in a network with a layered topology. During operation, the system uses a local shortest path tree (SPT) for a node in a network with a layered topology to identify one or more additional nodes in the network that are farthest from the node. Next, the system compares the local SPT with a remote SPT for the one or more additional nodes to identify a position of the node in the layered topology. The system then outputs the position of the node for use in configuring the operation of the node in the network.