Recent studies have shown that the composition of bacteria inside our bodies and in our environments play a significant role in our health. However, the interaction between the compositions of bacteria and our health remains mysterious, where research efforts are needed to reveal this relationship with proper analysis. In this study, we propose a new systems biology approach using split graphs to analyze inter-correlations among microbiome components and their corresponding impact on health and growth of organisms living in associated environments. The proposed model allows us to explore features of the bacteria in a given ecosystem, including their inter-correlations as well as how an active cluster of bacteria impact phenotypes of organisms in such an ecosystem. Further, the proposed model is flexible enough to allow the analysis of bacterial features and the impact on host phenotype together as well as individually. Extensive analytical work has been conducted, where the proposed model was tested using several case studies to elucidate impacts of composition of the microbiome on various host phenotypes, in particular, bacterial metabolic pathway. In the reported study, we used metagenomes from Crohn's disease patients in Korean populations and utilize an integrated bioinformatics pipeline to characterize the taxonomic and metabolic pathway composition. The results show that different groups of bacteria are significantly associated with various phenotypes related to metabolic pathways in patient samples as compared to healthy samples. This proposed split graph model has a great potential in assisting researchers to unravel mechanisms underlying complex biological systems and understand how various components in microbiomes affect the growth and health of organisms in such microbiomes.