  We investigate the classical and quantum networking regimes of the butterfly
network and a group of larger networks constructed with butterfly network
blocks. By considering simultaneous multicasts from a set of senders to a set
of receivers, we analyze the corresponding rates for transmitting classical and
quantum information through the networks. More precisely, we compare achievable
rates (i.e., lower bounds) for classical communication with upper bounds for
quantum communication, quantifying the performance gap between the rates for
networks connected by identity, depolarizing and erasure channels. For each
network considered, we observe a range over which the classical rate
non-trivially exceeds the quantum capacity. We find that, by adding butterfly
blocks in parallel, the difference between transmitted bits and qubits can be
increased up to one extra bit per receiver in the case of perfect transmission
(identity channels). Our aim is to provide a quantitative analysis of those
network configurations which are particularly disadvantageous for quantum
networking, when compared to classical communication. By clarifying the
performance of these 'negative cases', we also provide some guidance on how
quantum networks should be built.
