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.
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