The structure and dynamics of a typical biological system is complex due to the large number and variety of interactions between its parts. The investigation of such systems with classical mathematical tools, such as differential equations for their dynamics, is not always suitable. A graph theoretical (network) model may serve as a rough but powerful tool in such cases. In this talk, I will present my ongoing research on the structural and dynamical aspects of Transcriptional Gene Regulation. I will discuss the results obtained by using both model networks with different topologies and the available data for the Yeast, Saccharomices Cerevisiae.