  A main goal in the analysis of a complex system is to infer its underlying
network structure from time-series observations of its behaviour. The inference
process is often done by using bi-variate similarity measures, such as the
cross-correlation (CC), however, the main factors favouring or hindering its
success are still puzzling. Here, we use synthetic neuron models in order to
reveal the main topological properties that frustrate or facilitate inferring
the underlying network from CC measurements. Specifically, we use pulse-coupled
Izhikevich neurons connected as in the Caenorhabditis elegans neural networks
as well as in networks with similar randomness and small-worldness. We analyse
the effectiveness and robustness of the inference process under different
observations and collective dynamics, contrasting the results obtained from
using membrane potentials and inter-spike interval time-series. We find that
overall, small-worldness favours network inference and degree heterogeneity
hinders it. In particular, success rates in C. elegans networks -- that combine
small-world properties with degree heterogeneity -- are closer to success rates
in Erd\"os-R\'enyi network models rather than those in Watts-Strogatz network
models. These results are relevant to understand better the relationship
between topological properties and function in different neural networks.
