Two graphs are said to be cospectral if they have same eigenvalues wrt adjacency matrix, Normalised or Signless laplacian matrix. How many graphs has cospectral mates for a given number of nodes? We know answer to this question when number of nodes is less than $12$. I did not see any research paper till now where author has shown any algorithmic approach to compute those statistics. Either it is too simple to say or they do not wish to disclose it.

For a given number of nodes I like to compute number of graphs with at least one cospectral mate. Is there any algorithmic way to do so? If available please give me some references.

Thank you for your help.