Network structure plays a critical role in channeling person-to-person transmission of infectious disease agents like HIV. Stochastic simulations are used here to examine the effect of two structural attributes: concurrent partnerships (degree) and mixing patterns (degree-based homophily bias). Four alternative partnership scenarios are compared: (1) sequential monogamy, and concurrent partnerships with (2) random (3) assortative and (4) disassortative mixing by degree. Concurrent partnerships are found to dramatically increase the speed and pervasiveness of epidemic spread, and the implications for HIV transmission are discussed.