An empty graph on nodes consists of isolated nodes with no edges. Such graphs are sometimes also called edgeless graphs or null graphs (though the term "null graph" is also used to refer in particular to the empty graph on 0 nodes).

The empty graph on 0 nodes is (sometimes) called the null graph and the empty graph on 1 node is called the singleton graph. The empty graph on vertices is the graph complement of the complete graph , and is commonly denoted . The notation is apparently also used by some authors (e.g., Tyshkevich 2000, Fact 2), but not recommended as it conflicts with use of this notation for an odd graph among others.

The empty graph on nodes can be generated in the Wolfram Language as Graph[Range[n], ] or FromEntity[Entity["Graph", "Empty", n]], and precomputed properties of empty graphs are available in the Wolfram Language using GraphData["Empty", n].

The bipartite double graph of the empty graph is .

Empty graphs are (trivially) dominating unique.