  We derive asymptotic properties for a stochastic dynamic network model in a
stochastic dynamic population. In the model, nodes give birth to new nodes
until they die, each node being equipped with a social index given at birth.
During the life of a node it creates edges to other nodes, nodes with high
social index at higher rate, and edges disappear randomly in time. For this
model we derive criterion for when a giant connected component exists after the
process has evolved for a long period of time, assuming the node population
grows to infinity. We also obtain an explicit expression for the degree
correlation $\rho$ (of neighbouring nodes) which shows that $\rho$ is always
positive irrespective of parameter values in one of the two treated submodels,
and may be either positive or negative in the other model, depending on the
parameters.
