  A \textit{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 that 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 set-graphs and study the properties and
characteristics of set-graphs. We also check the primitive hole number and
primitive degree of set-graphs. Interesting introductory results on the nature
of order of set-graphs, degree of the vertices corresponding to subsets of
equal cardinality, the number of largest complete subgraphs in a set-graph etc.
are discussed in this study. A recursive formula to determine the primitive
hole number of a set-graph is also derived in this paper.
