# Average Vertex Degree of Connected Graphs

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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

## Snapshots

## Details

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.

## Permanent Citation

"Average Vertex Degree of Connected Graphs"

http://demonstrations.wolfram.com/AverageVertexDegreeOfConnectedGraphs/

Wolfram Demonstrations Project

Published: March 7 2011