  The way in which a social network is generated, in terms of how individuals
attach to each other, determines the properties of the resulting network. Here
we study an intuitively appealing `friend of a friend' model, where a network
is formed by each newly added individual attaching first to a randomly chosen
target and then to $n_q\geq 1$ randomly chosen friends of the target, each with
probability $0<q\leq1$. We revisit the master equation of the expected degree
distribution for this model, providing an exact solution for the case when
$n_q$ allows for attachment to all of the chosen target's friends (a case
previously studied by \cite{lambiotte2016}), and demonstrating why such a
solution is hard to obtain when $n_q$ is fixed (a case previously studied by
\cite{Levens2022}.) In the case where attachment to all friends is allowed, we
also show that when $q<q^*\approx0.5671$, the expected degree distribution of
the model is stationary as the network size tends to infinity. We go on to look
at the clustering behaviour and the triangle count, focusing on the cases where
$n_q$ is fixed.
