With developments in experimental connectomics producing wiring diagrams of many neuronal networks, there is emerging interest in theories to understand the relationship between structure and function. Efficiency of information flow in networks has been proposed as a key functional in characterizing cognition, and we have previously shown that information-theoretic limits on information flow are predictive of behavioral speed in the nematode Caenorhabditis elegans. In particular, we defined and computed a notion called effective bottleneck capacity that emerged from a pipelining model of information flow. It was unclear, however, whether the particular C. elegans connectome had unique capacity properties or whether similar properties would hold for random networks. Here, we determine the effective bottleneck capacity for several random graph ensembles to understand the range of possible variation and compare to the C. elegans network.