Abstract: Let $\mathbb{B}^W_{n,n+1}$ denote the set of bicyclic
weighted graphs of order $n$ with the weight set $W$. In this
article we determine the structure and some weight distribution of
the weighted bicyclic graph with the largest spectral radius in
$\mathbb{B}^W_{n,n+1}$ with a fixed weight set
$W=\{w_1,w_2,\ldots,w_{n+1}\}$, where $w_1\geqslant w_2\geqslant
\cdots \geqslant w_{n+1}>0$.

Key words: weighted bicyclic graph, spectral radius, maximum graph