Routing utilities currently present in cirq contrib expect a networkx graph of device (/target topology) where each node is a cirq.Qid. NamedTopology stores topology graphs where each node is a number / tuple.
TiltedSquareLattice has a nodes_to_gridqubits method which can provide a mapping from the graph nodes to the corresponding grid qubits.

This can be used to quickly get the graph needed for routing circuits from the topology graph as follows:

routing_graph = nx.relabel_nodes(topology.graph, topology.nodes_to_gridqubits())

A similar convenience method, nodes_to_linequbits, should be added to the LineQubit named topology as well.

cc @mpharrigan