The Colin de Verdière invariant 
of a nonempty finite simple
graph 
is the largest nullity of a real symmetric matrix 
indexed by its vertices satisfying
three conditions. Its off-diagonal entries are negative
on edges and zero on nonedges, it has exactly one negative eigenvalue counted
with multiplicity, and it has the strong
Arnold property. The diagonal entries are unrestricted (Colin de Verdière
1990).
The Colin de Verdière chromatic conjecture relates this invariant to the chromatic number. It differs from maximum nullity, whose defining matrix class does not impose the sign, eigenvalue, and strong Arnold property conditions.
