Most emerging infectious diseases (EIDs) in humans have arisen from animals. Identifying high-risk hosts is therefore vital for the control and surveillance of these diseases. Viewing hosts as connected through the parasites they share, we use network tools to investigate predictors of parasitism and sources of future EIDs. We generated host-parasite networks that link hosts when they share a parasite, using nonhuman primates as a model system because--owing to their phylogenetic proximity and ecological overlap with humans--they are an important source of EIDs to humans. We then tested whether centrality in the network of host species--a measurement of the importance of a given node (i.e., host species) in the network--is associated with that host serving as a potential EID source. We found that centrality covaries with key predictors of parasitism, such as population density and geographic range size. Importantly, we also found that primate species having higher values of centrality in the primate-parasite network harbored more parasites identified as EIDs in humans and had parasite communities more similar to those found in humans. These relationships were robust to the use of different centrality metrics and to multiple ways of controlling for variation in how well each species has been studied (i.e., sampling effort). Centrality may therefore estimate the role of a host as a source of EIDs to humans in other multispecific host-parasite networks.