  We consider a random graph process in which, at each time step, a new vertex
is added with m out-neighbours, chosen with probabilities proportional to their
degree plus a strictly positive constant. We show that the expectation of the
clustering coefficient of the graph process is asymptotically proportional to
log n/n. Bollob\'as and Riordan have previously shown that when the constant is
zero, the same expectation is asymptotically proportional to ((log n)^2)/n.
