Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community structure, while ensembles with high assortativity are much less biased towards clustering or community structure. Further, clustered networks can amplify small homophilic bias for trait assortativity. This marked asymmetry suggests that transitivity, rather than homophily, drives the standard nonsocial/social network dichotomy.