Rhythmical activity patterns are ubiquitous in nature. We study an oscillatory biological system: collective activity cycles in ant colonies. Ant colonies have become model systems for research on biological networks because the interactions between the component parts are visible to the naked eye, and because the time-ordered contact network formed by these interactions serves as the substrate for the distribution of information and other resources throughout the colony. To understand how the collective activity cycles influence the contact network transport properties, we used an automated tracking system to record the movement of all the individuals within nine different ant colonies. From these trajectories we extracted over two million ant-to-ant interactions. Time-series analysis of the temporal fluctuations of the overall colony interaction and movement rates revealed that both the period and amplitude of the activity cycles exhibit a diurnal cycle, in which daytime cycles are faster and of greater amplitude than night cycles. Using epidemiology-derived models of transmission over networks, we compared the transmission properties of the observed periodic contact networks with those of synthetic aperiodic networks. These simulations revealed that contrary to some predictions, regularly-oscillating contact networks should impede information transmission. Further, we provide a mechanistic explanation for this effect, and present evidence in support of it.