  We discuss a simplified version of the testing problem considered by Pelican
and Graham (2019): testing for interdependencies in preferences over links
among N (possibly heterogeneous) agents in a network. We describe an exact test
which conditions on a sufficient statistic for the nuisance parameter
characterizing any agent-level heterogeneity. Employing an algorithm due to
Blitzstein and Diaconis (2011), we show how to simulate the null distribution
of the test statistic in order to estimate critical values and/or p-values. We
illustrate our methods using the Nyakatoke risk-sharing network. We find that
the transitivity of the Nyakatoke network far exceeds what can be explained by
degree heterogeneity across households alone.
