  In this paper, we present a detailed analysis of the global clustering
coefficient in scale-free graphs. Many observed real-world networks of diverse
nature have a power-law degree distribution. Moreover, the observed degree
distribution usually has an infinite variance. Therefore, we are especially
interested in such degree distributions. In addition, we analyze the clustering
coefficient for both weighted and unweighted graphs.
  There are two well-known definitions of the clustering coefficient of a
graph: the global and the average local clustering coefficients. There are
several models proposed in the literature for which the average local
clustering coefficient tends to a positive constant as a graph grows. On the
other hand, there are no models of scale-free networks with an infinite
variance of the degree distribution and with an asymptotically constant global
clustering coefficient. Models with constant global clustering and finite
variance were also proposed. Therefore, in this paper we focus only on the most
interesting case: we analyze the global clustering coefficient for graphs with
an infinite variance of the degree distribution.
  For unweighted graphs, we prove that the global clustering coefficient tends
to zero with high probability and we also estimate the largest possible
clustering coefficient for such graphs. On the contrary, for weighted graphs,
the constant global clustering coefficient can be obtained even for the case of
an infinite variance of the degree distribution.
