  Let $G$ be a finite group. The solubility graph associated with the finite
group $G$, denoted by $\Gamma_{\cal S}(G)$, is a simple graph whose vertices
are the non-trivial elements of $G$, and there is an edge between two distinct
elements $x$ and $y$ if and only if $\langle x, y\rangle$ is a soluble subgroup
of $G$. In this paper, we examine some properties of solubility graphs.
