Geneticists and epidemiologists often observe that certain hereditary disorders cooccur in individual patients significantly more (or significantly less) frequently than expected, suggesting there is a genetic variation that predisposes its bearer to multiple disorders, or that protects against some disorders while predisposing to others. We suggest that, by using a large number of phenotypic observations about multiple disorders and an appropriate statistical model, we can infer genetic overlaps between phenotypes. Our proof-of-concept analysis of 1.5 million patient records and 161 disorders indicates that disease phenotypes form a highly connected network of strong pairwise correlations. Our modeling approach, under appropriate assumptions, allows us to estimate from these correlations the size of putative genetic overlaps. For example, we suggest that autism, bipolar disorder, and schizophrenia share significant genetic overlaps. Our disease network hypothesis can be immediately exploited in the design of genetic mapping approaches that involve joint linkage or association analyses of multiple seemingly disparate phenotypes.