  The structure-property hypothesis says that the properties of all materials
are determined by an underlying crystal structure. The main obstacle was the
ambiguity of conventional crystal representations based on incomplete or
discontinuous descriptors that allow false negatives or false positives. This
ambiguity was resolved by the ultra-fast Pointwise Distance Distribution (PDD),
which distinguished all periodic structures in the world's largest collection
of real materials (Cambridge Structural Database). The state-of-the-art results
in property predictions were previously achieved by graph neural networks based
on various graph representations of periodic crystals, including the Crystal
Graph with vertices at all atoms in a crystal unit cell. This work adapts the
Pointwise Distance Distribution for a simpler graph whose vertex set is not
larger than the asymmetric unit of a crystal structure. The new Distribution
Graph reduces mean-absolute-error by 0.6\%-12\% while having 44\%-88\% of the
number of vertices when compared to the crystal graph when applied on the
Materials Project and Jarvis-DFT datasets using CGCNN and ALIGNN. Methods for
hyper-parameters selection for the graph are backed by the theoretical results
of the Pointwise Distance Distribution and are then experimentally justified.
