  We explicitate the relation between Hamiltonians for networks of interacting
qubits in the XYZ model and graph Laplacians. We then study evolution in
networks in which all sites can communicate with each other. These are modeled
by the complete graph K_{n} and called all-to-all networks. It turns out that
K_{n} does not exhibit perfect state transfer (PST). However, we prove that
deleting an edge in K_{n} allows PST between the two non-adjacent sites, when n
is a multiple of four. An application is routing a qubit over n different
sites, by switching off the link between the sites that we wish to put in
communication. Additionally, we observe that, in certain cases, the unitary
inducing evolution in K_{n} is equivalent to the Grover operator.
