1. A method for calculating a network path in an interconnected multi-domain network, the method comprising: receiving a path setup request message for a new traffic flow in the network, wherein the path setup request message identifies a source node in one domain of the network and a destination node in a second domain of the network; determining a common ancestor hierarchical routing domain that includes ancestor nodes of both the source and destination nodes; calculating an inter-domain path from the ancestor node of the source node to the ancestor node of the destination node in the common ancestor hierarchical routing domain that determines, for each lower-level domain, border nodes in the domain from the source node to the destination node using a traffic engineering network database (“TEDB”) that stores network topology information for the common ancestor hierarchical routing domain; and for each bottom-level domain, calculating an intra-domain path between the border nodes that were determined for the domain.