I know that we can determine the number of connected components of a graph from the eigenvalues of its Laplacian matrix. My question is:
*Is there a way to understand the size of each connected component of a graph from its eigenvalues?*

For example: if a graph has 3 connected components two of which are maximal then can we determine this from the graph's spectrum?

Explanation of terminology:
By *maximal connected component*, I mean a connected component whose number of nodes at least greater (not strictly) than the number of nodes in every other connected component in the graph.