  We study a simple model of dynamic networks, characterized by a set preferred
degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$
and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As
a starting point, we consider a homogeneous population, where each node has the
same $\kappa$, and examine several forms of $w(k;\kappa)$, inspired by
Fermi-Dirac functions. Using Monte Carlo simulations, we find the degree
distribution in steady state. In contrast to the well-known Erd\H{o}s-R\'{e}nyi
network, our degree distribution is not a Poisson distribution; yet its
behavior can be understood by an approximate theory. Next, we introduce a
second preferred degree network and couple it to the first by establishing a
controllable fraction of inter-group links. For this model, we find both
understandable and puzzling features. Generalizing the prediction for the
homogeneous population, we are able to explain the total degree distributions
well, but not the intra- or inter-group degree distributions. When monitoring
the total number of inter-group links, $X$, we find very surprising behavior.
$X$ explores almost the full range between its maximum and minimum allowed
values, resulting in a flat steady-state distribution, reminiscent of a simple
random walk confined between two walls. Both simulation results and analytic
approaches will be discussed.
