Characterization of oriented graphs of rank 2.

Let D be an oriented graph, i.e., a digraph in which all arcs are not symmetric, with vertex set { 1 , ... , n }. The adjacency matrix A = (a i j) of D is the n × n matrix defined as a i j = 1 if ij is an arc of D and a i j = 0 if ij is not an arc of D. The rank of D is defined to be the rank of its adjacency matrix. In this paper, oriented graphs of rank 2 are characterized. [ABSTRACT FROM AUTHOR]