 Triangle variance in a binomial random graph

For the triangle count in a binomial random graph, distinct triangle indicators are independent unless they share an edge. A shared-edge pair has covariance $p^5(1-p)$, and there are $12\left(\genfrac{}{}{0ex}{}{n}{4}\right)$ ordered pairs of that type. The individual indicator variances give the first term. Equivalently,by counting ordered pairs according to the number of shared vertices.