  Let $G$ be a simple graph with vertex set $V(G) = \{v_1 ,v_2 ,\cdots ,v_n\}$.
The Harary matrix $RD(G)$ of $G$, which is initially called the reciprocal
distance matrix, is an $n \times n$ matrix whose $(i,j)$-entry is equal to
$\frac{1}{d_{ij}}$ if $i\not=j$ and $0$ otherwise, where $d_{ij}$ is the
distance of $v_i$ and $v_j$ in $G$. In this paper, we characterize graphs with
maximum spectral radius of Harary matrix in three classes of simple connected
graphs with $n$ vertices: graphs with fixed matching number, bipartite graphs
with fixed matching number, and graphs with given number of cut edges,
respectively.
