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The underlying anatomical structure is fundamental to the study of brain networks, but the role of brainstem from a structural perspective is not very well understood. We conduct a computational and graph-theoretical study of the human structural connectome incorporating a variety of subcortical structures including the brainstem. Our computational scheme involves the use of Python DIPY and Nibabel libraries to develop structural connectomes using 100 healthy adult subjects. We then compute degree, eigenvector, and betweenness centralities to identify several highly connected structures and find that the brainstem ranks highest across all examined metrics, a result that holds even when the connectivity matrix is normalized by volume. We also investigated some global topological features in the connectomes, such as the balance of integration and segregation, and found that the domination of the brainstem generally causes networks to become less integrated and segregated. Our results highlight the importance of including the brainstem in structural network analyses. [ABSTRACT FROM AUTHOR]