Cvetkovic D, Rowlinson P & Simic S (1993) A study of eigenspaces of graphs. Linear Algebra and Its Applications, 182, pp. 45-66. https://doi.org/10.1016/0024-3795%2893%2990491-6
We investigate the relationship between the structure of a graph and its eigenspaces. The angles between the eigenspaces and the vectors of the standard basis of Rn play an important role. The key notion is that of a special basis for an eigenspace called a star basis. Star bases enable us to define a canonical bases of Rn associated with a graph, and to formulate an algorithm for graph isomorphism.
Linear Algebra and Its Applications: Volume 182