linguistic:paraphrasing
Finding cospectral graphs

Almost all trees are cospectral, i.e., as the number of vertices grows, the fraction of trees for which there exists a cospectral tree goes to 1.

A pair of regular graphs are cospectral if and only if their complements are cospectral.

A pair of distance-regular graphs are cospectral if and only if they have the same intersection array.

Cospectral graphs can also be constructed by means of the Sunada method.

Another important source of cospectral graphs are the point-collinearity graphs and the line-intersection graphs of point-line geometries. These graphs are always cospectral but are often non-isomorphic.