The density of a simple graph is defined as the edge count 
divided by the possible number of edges in the graph, i.e.,
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the edge count of 
, 
the vertex count, and 
is a binomial coefficient.
The density of a simple graph therefore ranges from 0 (for an empty graph) to 1 (for a complete graph).
The density of the singleton graph 
is undefined since there are no possible edges for a 1-vertex
graph, making 
perplexingly both a complete graph and an empty
graph.
