  We obtain closed form expressions for the expected conditional degree
distribution and the joint degree distribution of the linear preferential
attachment model for network growth in the steady state. We consider the
multiple-destination preferential attachment growth model, where incoming nodes
at each timestep attach to $\beta$ existing nodes, selected by
degree-proportional probabilities. By the conditional degree distribution
$p(\ell| k)$, we mean the degree distribution of nodes that are connected to a
node of degree $k$. By the joint degree distribution $p(k,\ell)$, we mean the
proportion of links that connect nodes of degrees $k$ and $\ell$. In addition
to this growth model, we consider the shifted-linear preferential growth model
and solve for the same quantities, as well as a closed form expression for its
steady-state degree distribution.
