Generic maximum nullity of a graph

For a graph G of order n, the maximum nullity of G is defined to be the largest possible nullity over all real symmetric n × n matrices A whose (i, j)th entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. Maximum nullity and the related parameter minimum rank of the same set of matrices have been studied extensively. A new parameter, generic maximum nullity, is introduced. Generic maximum nullity provides insight into the structure of the null-space in a matrix realizing maximum nullity of a graph. It is shown that generic maximum nullity is bounded above by edge connectivity.