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We develop intuitive metrics for quantifying complex nucleating systems underconfinement. These are shown to arise naturally from the analysis of thetopological ring network, and are amenable for use as order parameters for suchsystems. Drawing inspiration from qualitative visual inspection, we introduce ageneral topological criterion for elucidating the ordered structures ofconfined water, using a graph theoretic approach. Our criterion is based onprimitive rings, and reinterprets the hydrogen-bond-network in terms of theseprimitives. This approach has no a priori assumptions, except the hydrogen bonddefinition, and may be used as an exploratory tool for the automated discoveryof new ordered phases. We demonstrate the versatility of our criterion byapplying it to analyse well-known monolayer ices. Our methodology is thenextended to identify the building blocks of one-dimensional $n$-sided prismaticnanoribbon ices.

A General Topological Network Criterion for Exploring the Structure of Icy Nanoribbons and Monolayers