Average Vertex Degree of Connected Graphs

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.