  Upcoming cosmological surveys will provide unprecedented amount of data,
which will require innovative statistical methods to maximize the scientific
exploitation. Standard cosmological analyses based on abundances, two-point and
higher-order statistics of cosmic tracers have been widely used to investigate
the properties of the cosmic web and Large Scale Structure. However, these
statistics can only exploit a subset of the entire information content
available. Our goal is thus to implement new data analysis techniques based on
machine learning to extract cosmological information through forward modelling,
by directly exploiting the spatial coordinates and other observed properties of
galaxies and galaxy clusters. Specifically, we investigated a new
representation of large-scale structure data in the form of graphs. This data
format can be directly fed to Graph Neural Networks, a recently proposed class
of supervised Deep Learning algorithms. We tested the method on dark matter
halo catalogues in different cosmologies, finding promising results. In
particular, the method can discriminate among different dark energy models with
high accuracy, through both binary classification ($99\%-$accuracy) and
multi-class classification ($97\%-$accuracy). Moreover, it provides constraints
on the value of $w_0$, through regression, with high precision.
