  Graphical functions are positive functions on the punctured complex plane
$\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize
a parametric integral representation for graphical functions due to Lam, Lebrun
and Nakanishi, which implies the real analyticity of graphical functions.
Moreover we prove a formula that relates graphical functions of planar dual
graphs.
