Visibility is a very important topic in computer graphics and especially in calculations of global illumination. Visibility determination, the process of deciding which surface can be seen from a certain point, has also problematic applications in biomedical engineering. The problem of visibility computation with mathematical tools can be presented as a visibility network. Instead of utilizing a 2D visibility network or graphs whose construction is well known, in this paper, a new method for the construction of 3D visibility graphs will be proposed. Drawing graphs as nodes connected by links in a 3D space is visually compelling but computationally difficult. Thus, the construction of 3D visibility graphs is highly complex and requires professional computers or supercomputers. A new method for optimizing the algorithm visibility network in a 3D space and a new method for quantifying the complexity of a network in DNA pattern recognition in biomedical engineering have been developed. Statistical methods have been used to calculate the topological properties of a visibility graph in pattern recognition. A new n-hyper hybrid method is also used for combining an intelligent neural network system for DNA pattern recognition with the topological properties of visibility networks of a 3D space and for evaluating its prospective use in the prediction of cancer.