structures, giving us libraries of millions of potentially interesting new materials. This sheer abundance of structures requires novel techniques from big-data research to shed light on the existing libraries, as well as to facilitate the search for materials with optimal properties.

In nanoporous materials the shape of the pores plays an essential role in the behavior of the material. Conventionally, pore structure is characterized by a set of traditional geometric descriptors such as pore volume, largest included sphere, surface area, etc. These descriptors can be successfully optimized to search for materials with similar overall thermodynamic properties, but, as we will show, they capture partial geometric features only and do not encode enough geometric information to enable detection of materials that have similar overall pore shapes. There are computational techniques to quantify the similarity between crystal structures.[@zhu161; @oga091] However, these algorithms are limited to identifying identical crystal structures, while we are interested in finding materials that may have different crystal structures or chemical compositions but similar pore geometries. Martin [*et al*]{}.[@mar121] developed Voronoi network representations of pore geometries, which are useful as fingerprints but do not capture details of the local pore structure. In this Letter, we develop a mathematical quantification 