Biological experiments can be set in order to detect the causes of diseases. However, they are expensive and time consuming. Recent developments in sequencing technologies help researchers to more easily reveal the underlying mechanisms of the diseases. In this study, we propose a combinatorial method to construct generic and core gene co-expression networks (GCNs) to discover the genes and their interactions related to colon cancer. We apply five gene network inference (GNI) algorithms and combine their estimations with Simple Majority Voting to specify the frequently inferred gene interactions and obtain the resulting GCNs on two different gene expression datasets. We then apply the intersection and union operators on these GCNS to derive the core and generic GCNs, respectively. The evaluation results of overlap analysis and topological features of GCNs for the colon cancer show that the networks produced with the proposed approach fit to the power-law degree distribution better.