The gut microbiome affects the health status of the host through complex interactions with the host's intestinal wall. These host-microbiome interactions spatially vary along the physical and chemical environment of the intestine, but these changes remain unknown. This study investigated these intricate relationships through a gene co-expression network analysis based on dual transcriptome profiling of different intestinal sites (cecum, transverse colon, rectum) of the primate common marmoset. We proposed a gene module extraction algorithm based on graph theory to find tightly interacting gene modules of the host and the microbiome from a vast co-expression network. The 27 gene modules identified by this method, which include both host and microbiome genes, not only produced results consistent with previous studies regarding the host-microbiome relationships, but also provided new insights into microbiome genes acting as potential mediators in host-microbiome interplays. Specifically, we discovered associations between the host gene FBP1, a cancer marker, and polysaccharide degradation-related genes (pfkA, fucI) coded by Bacteroides vulgatus, as well as relationships between host genes CD19, CD22, CD79B, PTPN6 involved in B-cell immune responses and a tryptophan synthesis gene (trpB) coded by Parabacteroides distasonis. Furthermore, our proposed module extraction algorithm surpassed existing approaches by successfully defining more functionally related gene modules, providing insights for understanding the complex relationship between the host and the microbiome.