  This paper is a step towards a systematic theory of the transitivity
(clustering) phenomenon in random networks. A static framework is used, with
adjacency matrix playing the role of the dynamical variable. Hence, our model
is a matrix model, where matrices are random, but their elements take values 0
and 1 only. Confusion present in some papers where earlier attempts to
incorporate transitivity in a similar framework have been made is hopefully
dissipated. Inspired by more conventional matrix models, new analytic
techniques to develop a static model with non-trivial clustering are
introduced. Computer simulations complete the analytic discussion.
