A random graph is a graph - a set of vertices and edges - that is chosen according to some probability distribution. In the most common model, $G_{n, p}$, a graph has $n$ vertices, and edges are present independently with probability $p$. Use (graphing-functions) instead if your question is about graphing or plotting functions.
A random graph is a graph that is chosen according to some probability distribution. The most common model is $G_{n, p}$. A graph with this distribution has $n$ vertices, and edges are present independently with probability $p$. A closely related model is $G_{n,m}$. In this model, a graph on $n$ vertices is chosen uniformly among all graphs with $m$ edges.