Let $G$ be a random graph generated as follows:- each vertex $i$ of the vertex set $\{1,\ldots,n\}$ has an associated random variable $X_i$ where $\{X_i : i \ge 1\}$ are i.i.d. Two vertices $i$ and $j$ are connected by an edge if and only if, $X_i + X_j > \theta$ where $\theta$ is a given threshold value. We study some properties of this graph $G$.