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 nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other.

中文翻译：

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图特征向量的节点域大小

考虑G（n，p）图的邻接矩阵的特征向量。节点域是该特征向量具有恒定符号的一组顶点的连接分量。众所周知，每个特征向量正好有两个节点域对应于一个非引导特征值。我们证明这些节点域的大小很有可能彼此相等。