A 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 setgraphs. We also check the primitive hole number and primitive degree of set-graphs. Interesting introductory results on the nature of order of setgraphs, 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.

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