  Apart from the role the clustering coefficient plays in the definition of the
small-world phenomena, it also has great relevance for practical problems
involving networked dynamical systems. To study the impact of the clustering
coefficient on dynamical processes taking place on networks, some authors have
focused on the construction of graphs with tunable clustering coefficients.
These constructions are usually realized through a stochastic process, either
by growing a network through the preferential attachment procedure, or by
applying a random rewiring process. In contrast, we consider here several
families of static graphs whose clustering coefficients can be determined
explicitly. The basis for these families is formed by the $k$-regular graphs on
$N$ nodes, that belong to the family of so-called circulant graphs denoted by
$C_{N,k}$. We show that the expression for the clustering coefficient of
$C_{N,k}$ reported in literature, only holds for sufficiently large $N$. Next,
we consider three generalizations of the circulant graphs, either by adding
some pendant links to $C_{N,k}$, or by connecting, in two different ways, an
additional node to some nodes of $C_{N,k}$. For all three generalizations, we
derive explicit expressions for the clustering coefficient. Finally, we
construct a family of pairs of generalized circulant graphs, with the same
number of nodes and links, but with different clustering coefficients.
