Average Vertex Degree of Connected Graphs
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Although simple, the average vertex degree of a connected graph is quite interesting. For example, in graphs where the vertex degree is constant, the number of nodes reached by extending out nodes from a single node is . For graphs where the vertex degrees are not all the same, and taking all vertices into account, the value of , where is the average vertex degree, provides another similar perspective.
Contributed by: John Cicilio (March 2011)
Open content licensed under CC BY-NC-SA
For more information on the degree of a vertex of a graph, see http://en.wikipedia.org/wiki/Degree_%28 graph_theory %29.For more on degree distribution, see http://en.wikipedia.org/wiki/Degree_distribution.
"Average Vertex Degree of Connected Graphs"
Wolfram Demonstrations Project
Published: March 7 2011