Conditions that alter Graph Density
Density does not show where edges are located or whether the graph is connected.
Working through Graph Density with numbers
Four edges among five vertices give density 4/10=0.4.
Undirected simple-graph density is |E| divided by C(|V|,2), ranging from zero to one.
The roles assigned to vertices and undirected edges explain the operation that produces graph density.
When to reach for Graph Density
It compares network sparsity, collaboration, connectivity potential, and graphs of different sizes. Graph Density also relates to local connectivity.
Count distinct edges, compute the complete-graph maximum, and divide the two counts. Graph Density also connects to maximum edges.
An independent Graph Density pass needs Vertices plus Undirected edges. Judge whether Graph density has a plausible sign and scale. Test Undirected edges separately; otherwise the cause of a changed Graph Density Graph density remains unclear.
Reproducing Graph Density later
How Graph Density changes
Adding one edge increases density by exactly 1/C(n,2) while the vertex set is fixed. That behavior gives the graph density output a built-in reasonableness test.
Recording Graph Density
A reusable answer should be named Graph Density and retain the finite setup that defines it. For reproduction, the supplied fields and defining rule are more informative than the Graph Density label alone.
The complete-graph page supplies the denominator directly. Writing “Graph density” beside the output prevents that mix-up.
Checking the denominator
For n vertices the maximum is n(n−1)/2; the reported ratio must remain between zero and one.
Compare the edge count with the complete-graph maximum before dividing. A result of zero describes an empty graph and one describes a complete graph; neither endpoint alone says whether the chosen vertices form one connected component.