Given a simple graph G = (V-G, E-G) with vertex set V-G and edge set E-G , the mixed graph (C) over tilde is obtained from G by orienting some of its edges. Let H(G)over tilde>) denote the Hermitian adjacency matrix of (G)over tilde> and A(G) be the adjacency matrix of G. The H-rank (resp. rank) of (G ) over tilde (resp. G), written as rk(G) (resp. r(G)), is the rank of H(G) (resp. A(G)). Denote by d(G) the dimension of cycle space of G, that is d(G) = vertical bar E-G vertical bar - vertical bar V-G vertical bar + omega(G), where omega(G) denotes the number of connected components of G. In th...
