The relation between the Jordan structure of a matrix and its graph

AbstractIt is shown that the height characteristics of a matrix A strongly majorizes the dual sequence of the sequence of differences of maximal cardinalities of nonclosable k-paths in G(A), and that in the generic case the height characteristics is equal to that dual sequence. Simultaneously, it is shown that the sequence of differences of minimal kth nonclosable norms of path coverings for a directed graph G is the dual of the sequence of differences of maximal cardinalities of nonclosable k-paths in G. These results generalize both matrix theoretical and graph theoretical known results for the triangular case