The low prevalence rate of orphan diseases (OD) requires special combined efforts to improve diagnosis, prevention, and discovery of novel therapeutic strategies. To identify and investigate relationships based on shared genes or shared functional features, we have conducted a bioinformatic-based global analysis of all orphan diseases with known disease-causing mutant genes. Starting with a bipartite network of known OD and OD-causing mutant genes and using the human protein interactome, we first construct and topologically analyze three networks: the orphan disease network, the orphan disease-causing mutant gene network, and the orphan disease-causing mutant gene interactome. Our results demonstrate that in contrast to the common disease-causing mutant genes that are predominantly nonessential, a majority of orphan disease-causing mutant genes are essential. In confirmation of this finding, we found that OD-causing mutant genes are topologically important in the protein interactome and are ubiquitously expressed. Additionally, functional enrichment analysis of those genes in which mutations cause ODs shows that a majority result in premature death or are lethal in the orthologous mouse gene knockout models. To address the limitations of traditional gene-based disease networks, we also construct and analyze OD networks on the basis of shared enriched features (biological processes, cellular components, pathways, phenotypes, and literature citations). Analyzing these functionally-linked OD networks, we identified several additional OD-OD relations that are both phenotypically similar and phenotypically diverse. Surprisingly, we observed that the wiring of the gene-based and other feature-based OD networks are largely different; this suggests that the relationship between ODs cannot be fully captured by the gene-based network alone.