A Central Limit Theorem for the Number of Edges in the Random Intersection of Two Graphs

Abstract

The distribution of the statistic $X$ which is the number of edges in the intersection graph $G_1 \cap G_2(V, E_1 \cap E_2)$ of $G_1(V, E_1)$ and $G_2(V, E_2)$ is investigated through its moments. An expression is obtained for the $r$th central moment and the moment ratios of $X$ are, under a set of sufficient conditions, shown to approximate to those of a normal variable with the standardised variable. $Z = \{X - \epsilon(X)\}/(\operatorname{var} (X))^{\frac{1}{2}}$ having an asymptotically unit normal distribution.