The two important problems of computational biology are the modeling of gene regulatory networks and the study of the network structure of complex biological systems. There is an increased use of mathematical and computational theory techniques to solve both these problems. The Boolean circuit model is one of the most popular modeling paradigms used to model gene regulatory networks. In this paper we try to make use of the properties of threshold logic (an alternative to Boolean logic to design digital circuits) to determine the network structure of gene systems. This approach uses the gene-expression data from microarray experiments as input. The proposed method was first used to build the gene network for a set of genes, proteins, and other molecular components based on in silico data. Then, the method was applied to a biological dataset to build the gene regulatory network for a core set of genes associated with melanoma. Some of the interactions found could be verified by earlier biological experiments reported in published literature. Other interactions that could not be validated by existing biological knowledge can provide insights into the investigation of bio-chemical pathways associated with melanoma development.