Transcription factors are proteins that play a key role in the control of gene transcription in cells. Understanding how this control works would be of immense value in many areas of biology and medicine. However, the transcription control process is complex, and transcription factors are only a part of a much more complex and dynamic system. This system is noisy and poorly understood, with numerous components. The focus of this thesis is specifically on the regulation of the transcription factors. We narrowed down this focus to only include in the system's model the transcriptional control of the regulation of transcription factors by themselves. We omit from this research other aspects of the process, such as miRNA. Our main research question is centred on determining how much of the observed cellular behaviour can be modelled with this simplified system. The regulation of transcription factors by transcription factors can be expressed as a network. We made a realistic network based on real world data obtained from TRANSFAC and TRRUST, two databases that describe the interactions between transcription factors and their target proteins for the human model. Furthermore, we applied the same model in yeast to corroborate the results, basing the network on the YEASTRACT database. The mathematical modelling of the system takes the model proposed by Han in 2013, and applies it to the networks. We modified this model to take into account the fact that these processes occur inside the cell nucleus, and are therefore constrained by the small size and finite quality of the nucleus. The model validity was tested by exploring how the network responds when the transcription factors are perturbed, and by comparing this with real world data from when transcription factors change, specifically in cancers and rare genetic diseases. As part of these processes, we developed two models for measuring the impact given a perturbation of a network. The first model is based on the Euclidean distance between the original and the perturbed network, while the second model uses the topological characteristics of the network to predict the impact of the perturbation. We further analyse the impact, network topological characteristics, and a measure of network centrality. Interestingly, we found significant correlations between the behaviour of the model system with the data from cancer and rare genetic diseases. This has provided support to the adequacy of our simplified model. Moreover, the yeast model also presented significant correlation of the behaviour of the model system with phenotypes. In building the networks, we observed that there were significant examples of transcription factor auto-regulation (which we call self-loops in the network model) in both models. Such autoregulation has been extensively studied mathematically in systems control theory, and biologically in prokaryotic systems, with fewer studies in eukaryotes. From the model analysis, we were able to develop new theories related to the importance of these self-loops in transcription factor networks. This has some potential applications in the prediction of the impact of variants in transcription factor binding sites in genetic medicine.