  A \emph{primitive hole} of a graph $G$ is a cycle of length 3 in $G$. The
number of primitive holes in a given graph $G$ is called the primitive hole
number of the graph $G$. The primitive degree of a vertex $v$ of a given graph
$G$ is the number of primitive holes incident on the vertex $v$. In this paper,
we introduce the notion of Pythagorean holes of graphs and initiate some
interesting results on Pythagorean holes in general as well as results in
respect of set-graphs and Jaco graphs.
