In a 2D network with uniform node density $\rho$, each node has an average of $n_1 = \rho \pi R^2$ one-hop neighbors and $n_2 \leq 3 \rho \pi R^2$ two-hop neighbors. Each of these 1-hop neighbors randomly selects 4 out of their direct neighbors.
I am working in a problem where I want to find the expected number of unique two-hop neighbors for a specific node $x$ after all its one-hop neighbors have made their selections.
(Assuming the network is large enough to ignore edge effects and each selection is independent.)