In this paper we study the following problem: \emph{Let $(X,d)$ be a complete metric space and $f:X\to X$ be a mapping. Which metric conditions imposed on $f$ imply that: \begin{itemize} \item [$(i)$] $f$ is a graphic contraction ? \item [$(ii)$] $f$ is a weakly Picard mapping ? \end{itemize} }