  When two graphs have a correlated Bernoulli distribution, we prove that the
alignment strength of their natural bijection strongly converges to a novel
measure of graph correlation $\rho_T$ that neatly combines intergraph with
intragraph distribution parameters. Within broad families of the random graph
parameter settings, we illustrate that exact graph matching runtime and also
matchability are both functions of $\rho_T$, with thresholding behavior starkly
illustrated in matchability.
