Gene-Gene dependency plays a very important role in system biology as it pertains to the crucial understanding of dierent biological mechanisms. High-throughput data provides a new platform useful to reveal the dynamic mechanism of gene-gene dependencies. In this talk, we will discuss three dierent approaches to construct a gene network. First we will review the model selection strategies in the construction of Bayesian network. Secondly we will discuss the constrained optimization problem in the modelling of Gaussain Graphical model. Third, we will discuss the choice of appropriate measure for gene-gene interaction for time series data. Various biological data set are analyzed to demonstrate the application of those methods and their implications in understanding the inherent biological mechanisms in cancer cell lines.