Pedigree inference, for example determining whether two persons are second cousins or unrelated, can be done by comparing their genotypes at a selection of genetic markers. When the data for one or more of the persons is from low-coverage next generation sequencing (lcNGS), currently available computational methods either ignore genetic linkage or do not take advantage of the probabilistic nature of lcNGS data, relying instead on first estimating the genotype. We provide a method and software (see familias.name/lcNGS) bridging the above gap. Simulations indicate how our results are considerably more accurate compared to some previously available alternatives. Our method, utilizing a version of the Lander-Green algorithm, uses a group of symmetries to speed up calculations. This group may be of further interest in other calculations involving linked loci.