Large multipartite quantum systems tend to rapidly reach extraordinary levels
of complexity as their number of constituents and entanglement links grow. Here
we use complex network theory to study a class of continuous variables quantum
states that present both multipartite entanglement and non-Gaussian statistics.
In particular, the states are built from an initial imprinted cluster state
created via Gaussian entangling operations according to a complex network
structure. To go beyond states that can be easily simulated via classical
computers we engender non-Gaussian statistics via multiple photon subtraction
operations. We then use typical networks measures, the degree and clustering,
to characterize the emergent complex network of photon-number correlations
after photon subtractions. We show that, in contrast to regular clusters, in
the case of imprinted complex network structures the emergent correlations are
strongly affected by photon subtraction. On the one hand, we unveil that photon
subtraction universally increases the average photon-number correlations,
regardless of the imprinted network structure. On the other hand, we show that
the shape of the distributions in the emergent networks after subtraction is
greatly influenced by the structure of the imprinted network, as witnessed by
their higher-moments. Thus for the field of network theory, we introduce a new
class of networks to study. At the same time for the field of continuous
variable quantum states, this work presents a new set of practical tools to
benchmark systems of increasing complexity.Comment: 25 pages (incl. appendix), 17 figure