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Ecological associations between hosts and parasites are influenced by host exposure and susceptibility to parasites, and by parasite traits, such as transmission mode. Advances in network analysis allow us to answer questions about the causes and consequences of traits in ecological networks in ways that could not be addressed in the past.We used a network‐based framework (exponential random graph models or ERGMs) to investigate the biogeographic, phylogenetic and ecological characteristics of hosts and parasites that affect the probability of interactions among nonhuman primates and their parasites. Parasites included arthropods, bacteria, fungi, protozoa, viruses and helminths.We investigated existing hypotheses, along with new predictors and an expanded host–parasite database that included 213 primate nodes, 763 parasite nodes and 2319 edges among them. Analyses also investigated phylogenetic relatedness, sampling effort and spatial overlap among hosts.In addition to supporting some previous findings, our ERGM approach demonstrated that more threatened hosts had fewer parasites, and notably, that this effect was independent of hosts also having a smaller geographic range. Despite having fewer parasites, threatened host species shared more parasites with other hosts, consistent with loss of specialist parasites and threat arising from generalist parasites that can be maintained in other, non‐threatened hosts. Viruses, protozoa and helminths had broader host ranges than bacteria, or fungi, and parasites that infect non‐primates had a higher probability of infecting more primate species.The value of the ERGM approach for investigating the processes structing host–parasite networks provided a more complete view on the biogeographic, phylogenetic and ecological traits that influence parasite species richness and parasite sharing among hosts. The results supported some previous analyses and revealed new associations that warrant future research, thus revealing how hosts and parasites interact to form ecological networks. [ABSTRACT FROM AUTHOR]