The ultimate goal of genomics research is to describe the network of molecules and interactions that govern all biological functions and disease processes in cells. Nonlinear interactions among genes in terms of their logic relationships play a key role for deciphering the networks of molecules that underlie cellular function. We present a method based on a graph coloring scheme and information theory to identify the gene expression network with lower and higher order logic interactions of genes. The analysis of oncogenes and suppressor genes from a colon cancer mRNA microarray dataset identifies a gene expression network with directionality and weights that reflects intracellular communication pathways. The success of the proposed method in mining hidden, complicated gene interactions and reliably interpreting experimental results suggests that the proposed method is a useful tool for understanding cancer systems. Extension of this method holds the potential to be fruitful for understanding other complex, nonsymmetric systems.