ELA, Volume 9, pp. 255-269, September 2002, abstract.
The Combinatorial Structure of Eventually Nonnegative Matrices
Sarah Carnochan Naqvi and Judith J. McDonald
In this paper it is shown that an eventually nonnegative
matrix A whose index of zero is less than or equal to one,
exhibits many of the same combinatorial properties as a
nonnegative matrix. In particular, there is a positive integer
g such that A^g is nonnegative, A and A^g have the same
irreducible classes, and the transitive closure of the
reduced graph of A is the same as the transitive closure
of the reduced graph of A^g. In this instance, many of the
combinatorial properties of nonnegative matrices carry over
to this subclass of the eventually nonnegative matrices.