Alignment Strength and Correlation for Graphs [article]

Donniell E. Fishkind, Lingyao Meng, Ao Sun, Carey E. Priebe, Vince Lyzinski
2020 arXiv   pre-print
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 ρ_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 ρ_T, with thresholding behavior starkly illustrated in matchability.
arXiv:1808.08502v4 fatcat:6lvegm4ydzfjvdeuukl2uuyd5e