Characterization of oriented graphs of rank 2

Abstract 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.