WOLFRAM|DEMONSTRATIONS PROJECT

Average Vertex Degree of Connected Graphs

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graph index
1
rotatable
name:
12P2+3K1
average vertex degree:
2

Although simple, the average vertex degree of a connected graph is quite interesting. For example, in graphs where the vertex degree
K
is constant, the number of nodes reached by extending out
r
nodes from a single node is
r
K
. For graphs where the vertex degrees are not all the same, and taking all vertices into account, the value of
r
A
, where
A
is the average vertex degree, provides another similar perspective.