Complex networks is a new emerging branch of random graph theory. For a long time random graphs have been mainly studied by pure mathematics but recently due to the availability of empirical data on real-world networks they have attracted the attention of physics and natural sciences. Methods of statistical physics, both empirical and theoretical, have thus begun to play an important role in this research area.

The empirical observations of real-networks have had a feedback on theoretical development which now concentrated on the understanding of the observed features, for example: fat tails in node degree distribution, small world effect, degree-degree correlations or high clustering.

In this talk we concentrate on the issue of clustering. We propose a systematic approach to theory of clustering. We discuss a model of weighted random graphs with a statistical weight favoring triangular loops. Using a perturbative expansion we show the existence of a perturbative phase with a non-trivial clustering. We test results of the perturbation theory against Monte-Carlo simulations. We also discuss clustering for scale-free networks.

Marian Smoluchowski Institute of Physics, Krakow