Eigenvectors of a large Graph

Question

Please i am working on a graph with a huge number of vertices, and i have a particular eigenvalue having and eigen space of dimension 19, What is the best way to find the eigen vectors. Here is what i have done: I have already used the matrix B and i got an eigen vector which i extend to an eigen vector of the adjacency matrix A using the Px formula where x is an eigen vector for B and P is the characteristic matrix of the distance partitions (Using the reasoning of equitable partitions). But ow can i more generally get a basis for the eigen space?

Answer 1

First, 72 is a small number of vertices. Second, a strongly regular graph on $p+1$ vertices (where $p$ is prime) is either the disjoint union of complete graphs, or is the complement of such a graph.