  Let $G$ be a connected graph and $Q(G)$ be the signless Laplacian of $G$. The
principal ratio $\gamma(G)$ of $Q(G)$ is the ratio of the maximum and minimum
entries of the Perron vector of $Q(G)$. In this paper, we consider the maximum
principal ratio $\gamma(G)$ among all connected graphs of order $n$, and show
that for sufficiently large $n$ the extremal graph is a kite graph obtained by
identifying an end vertex of a path to any vertex of a complete graph.
