Diffusion over a network depends crucially on the pattern and timing of relations. This is particularly important for diseases carried over networks with relatively low volume and turnover. Here we explore both aspects using simulation tools. First, we ask how the shape of the distribution of number of partners affects multiple connectivity, and second we measure the exposure potential in dynamic networks across a wide array of structural patterns to identify the influence of "concurrency," the overlap in time of interactions among network nodes. We find that concurrency in low-volume settings has the same effect on epidemic spreading as a structural increase in the average degree.