Abstract: In social network analysis the mean nodal degree and
density of the graph can be considered as a measure of the activity of
all actors in the network and this is an important property of a graph
and for making comparisons among networks. Since subjects in a
family or organization are subject to common environment factors, it
is prime interest to study the association between responses.
Therefore, we study the distribution of the mean nodal degree and
density of the graph under correlated binary units. The cross product
ratio is used to capture the intra-units association among subjects.
Computer program and an application are given to show the benefits
of the method.