  Consider an eigenvector of the adjacency matrix of a G(n, p) graph. A nodal
domain is a connected component of the set of vertices where this eigenvector
has a constant sign. It is known that with high probability, there are exactly
two nodal domains for each eigenvector corresponding to a non-leading
eigenvalue. We prove that with high probability, the sizes of these nodal
domains are approximately equal to each other.
