  Liquid water, besides being fundamental for life on Earth, has long
fascinated scientists due to several anomalies. Different hypotheses have been
put forward to explain these peculiarities. The most accredited one foresees
the presence in the supercooled region of two phases at different densities:
the low-density liquid phase and the high-density liquid phase. In our previous
work [Faccio et al., J. Mol. Liq. 355 (2022): 118922], we showed that it is
possible to identify these two forms in water networks through a computational
approach based on molecular dynamics simulation and on the calculation of the
total communicability of the associated graph, in which the nodes correspond to
water molecules and the edges represent the connections (interactions) between
molecules. In this paper, we present a more in-depth investigation of the
application of graph-theory based approaches to the analysis of the structure
of water networks. In particular, we investigate different connectivity and
centrality measures and we report on the use of a variety of global metrics
aimed at giving a topological and geometrical characterization of liquid water.

Numerical Analysis;Soft Condensed Matter;Numerical Analysis;Combinatorics