Point pattern analysis through proximity graphs

Spatial point patterns appear in many fields of research, including physics (arrangement of atoms in solids), ecology (location of plants or animals) and biology (cells in a tissue). The proximity graph of a point set is constructed by connecting neighbouring points. β-skeletons are a parametrized family of such graphs with many convenient mathematical properties, such as certain guarantees on connectedness and planarity (in the two-dimensional case). We develop a new method for characterizing spatial point patterns by first constructing the points’ β-skeleton, then describing its network properties. We show that this analysis technique can reveal different types of features of the point set than what common existing point pattern analysis methods are sensitive to, and demonstrate its use on biological datasets. Finally, we investigate the use of proximity graphs as null models for spatial networks.