This research uses random networks as benchmarks for inferential tests of network structures. Specifically, we develop formulas for expected values and confidence intervals for four frequently employed social network centrality indices. The first study begins with analyses of stylized networks, which are then perturbed with increasing levels of random noise. When the indices achieve their values for fully random networks, the indices reveal systematic relationships that generalize across network forms. The second study then delves into the relationships between numbers of actors in a network and the density of a network for each of the centrality indices. In doing so, expected values are easily calculated, which in turn enable chi-square tests of network structure. Furthermore, confidence intervals are developed to facilitate a network analyst’s understanding as to which patterns in the data are merely random, versus which are structurally significantly distinct.