  We establish asymptotic vertex degree distribution and examine its relation
to the clustering coefficient in two popular random intersection graph models
of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132].
For sparse graphs with a positive clustering coefficient, we examine
statistical dependence between the (local) clustering coefficient and the
degree. Our results are mathematically rigorous. They are consistent with the
empirical observation of Foudalis et al. [In Algorithms and Models for Web
Graph (2011) Springer] that, "clustering correlates negatively with degree."
Moreover, they explain empirical results on $k^{-1}$ scaling of the local
clustering coefficient of a vertex of degree k reported in Ravasz and Barabasi
[Phys. Rev. E 67 (2003) 026112].
