uses rules vw to specify the graph g.
Details and Options
- GraphDensity is the ratio of the number of edges divided by the number of edges of a complete graph with the same number of vertices.
- A simple undirected graph with vertices and edges has graph density .
- A simple directed graph with vertices and edges has graph density .
Examplesopen allclose all
Basic Examples (2)
Compute the density of a graph:
Graph density distribution of the Bernoulli graph model:
GraphDensity works with undirected graphs:
Use rules to specify the graph:
GraphDensity works with large graphs:
Find the proportion of games between teams during an American college football season:
Compute the probability that two randomly chosen friends in a network are connected:
Model a social network:
Simulate the model:
Analyze the model:
The expected number of edges matches the original graph:
Distribution of density in BernoulliGraphDistribution[n,p]:
The expected value is p:
Properties & Relations (6)
GraphDensity measures the density of the AdjacencyMatrix:
Get the density from AdjacencyMatrix:
The graph density is between 0 and 1:
The density of an empty graph is 0:
Use EmptyGraphQ to test for emptiness:
The density of a complete graph is 1:
Use CompleteGraphQ to test for complete graphs:
Converting an undirected graph to a directed graph does not change the density:
Unless self-loops are taken into consideration:
LocalClusteringCoefficient gives a local measure of density:
Introduced in 2012
Updated in 2015