Relation between the H-rank of a mixed graph and the rank of its underlying graph

Chen Chen, Shuchao Li, Minjie Zhang

Given a simple graph $G=(V_G,E_G)$ with vertex set $V_G$ and edge set $E_G$, the mixed graph $\tilde{G}$ is obtained from $G$ by orienting some of its edges. Let $H(\widetilde…