computations and in the use of graph eigenvalue methods to understand the spread of quantum information [@YangWang2003]. GHZ state preparation and state transfer are just two possible benchmark tasks, and it is possible that other tasks would result in different evaluations of relative performance between graphs.

Our work should also be considered in the context of classical network theory, where much is known about complicated graph structures [@Watts1998; @Barabasi1999; @Albert2002]. It remains to be seen to what degree classical network theory can be easily exported to the quantum domain. Quantum effects such as the no-cloning theorem may limit our ability to distribute information, or conversely we can take advantage of teleportation to distribute quantum bandwidth in anticipation of it actually being needed. As further examples of how quantum and classical networks differ, it has been shown that entanglement swapping may be used to permit quantum networks to reshape themselves into interesting and useful topologies [@Perseguers2010]. It has also been shown that, in general, the optimal strategy for entanglement generation in quantum networks can be difficult to calculate because many aspects of classical control theory do not apply [@DiFranco2012].

The structure of this paper is as follows. In \[sec:hp\], we will 