  The $\ell$-Rauzy graph of order $k$ for any infinite word is a directed graph
in which an arc $(v_1,v_2)$ is formed if the concatenation of the word $v_1$
and the suffix of $v_2$ of length $k-\ell$ is a subword of the infinite word.
In this paper, we consider one of the important aperiodic recurrent words, the
infinite Fibonacci word for discussion. We prove a few basic properties of the
$\ell$-Rauzy graph of the infinite Fibonacci word. We also prove that the
$\ell$-Rauzy graphs for the infinite Fibonacci word are strongly connected.
