Attention Deficit Hyperactivity Disorder (ADHD) is an increasingly prevalent neuropsychiatric disorder characterized by hyperactivity, inattention, and impulsivity. Symptoms emerge from underlying deficiencies in neurocircuitry, and recent research has suggested a role played by the gut microbiome. The gut microbiome is a complex ecosystem of interdependent taxa with an exponentially complex web of interactions involving these taxa, plus host gene and reaction pathways, some of which involve neurotransmitters with roles in ADHD neurocircuitry. Studies have analyzed the ADHD gut microbiome using macroscale metrics such as diversity and composition, and have proposed several biomarkers. Few studies have delved into the complex underlying dynamics ultimately responsible for the emergence of such metrics, leaving a largely incomplete, sometimes contradictory, and ultimately inconclusive picture. We aim to help complete this picture by venturing beyond taxa abundances and into taxa relationships (i.e. cooperation and competition), using a publicly available gut microbiome dataset from 30 Control (15 female, 15 male) and 28 ADHD (15 female, 13 male) undergraduate students. We conduct our study in two parts. We first perform the same macroscale analyses prevalent in ADHD gut microbiome literature (diversity, differential, biomarker, and composition) to observe the degree of correspondence, or any new trends. We then estimate two-way ecological relationships by producing Control and ADHD Microbial Co-occurrence Networks (MCNs), using SparCC correlations (p < 0.01). We perform community detection to find clusters of taxa estimated to mutually cooperate along with their centroids, and centrality calculations to estimate taxa most vital to overall gut ecology. We conclude by summarizing our results, and provide conjectures on how they can guide future experiments, some methods for improving our experiments, and general implications for the field.