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

Size of nodal domains of the eigenvectors of a G(n,p) graph