Genomic information can accurately specify relationships among animals, including between those without known common ancestors. Genetic variances estimated with genomic data relate to unknown, more distant, founder populations than those defined by the pedigree. Starting from different sets of assumptions, the properties of some alternative genomic relationship matrices (G) are explored. Although the assumptions and matrices differ, the resulting sets of estimated breeding values predict the differences between animals identically, despite obtaining different estimates of the additive genetic variance - showing that there are many ways of building G that provide identical results. For some methods integer and logic, rather than floating point, operations will expedite building G many-fold.