  This paper introduces a simple measure of a concordance pattern among
observed outcomes along a network, i.e., the pattern in which adjacent outcomes
tend to be more strongly correlated than non-adjacent outcomes. The graph
concordance measure can be generally used to quantify the empirical relevance
of a network in explaining cross-sectional dependence of the outcomes, and as
shown in the paper, can also be used to quantify the extent of homophily under
certain conditions. When one observes a single large network, it is nontrivial
to make inference about the concordance pattern. Assuming dependency graph,
this paper develops a permutation-based confidence interval for the graph
concordance measure. The confidence interval is valid in finite samples when
the outcomes are exchangeable, and under the dependency graph assumption
together with other regularity conditions, is shown to exhibit asymptotic
validity. Monte Carlo simulation results show that the validity of the
permutation method is more robust to various graph configurations than the
asymptotic method.
