  In this paper, we investigate the global clustering coefficient (a.k.a
transitivity) and clique number of graphs generated by a preferential
attachment random graph model with an additional feature of allowing edge
connections between existing vertices. Specifically, at each time step $t$,
either a new vertex is added with probability $f(t)$, or an edge is added
between two existing vertices with probability $1-f(t)$. We establish
concentration inequalities for the global clustering and clique number of the
resulting graphs under the assumption that $f(t)$ is a regularly varying
function at infinity with index of regular variation $-\gamma$, where $\gamma
\in [0,1)$. We also demonstrate an inverse relation between these two
statistics: the clique number is essentially the reciprocal of the global
clustering coefficient.
