One of the hallmarks of inter-regional functional coupling (IRFC) using fMRI is the distinctive and reproducible community structure that emerges after partitioning voxels into regions and regions into large scale sub-networks such as that of Yeo et. al. 2011. To the extent that IRFC in functional brain networks from any modality reects capacity for neurophysiological communication, the strength of coupling between two large scale communities, such as the default mode sub-network (DMN) and fronto-parietal control sub-network (FPN) in Fig 1a., is a vital index of possible reconguration of community structure. Changes to community strength may vary between individuals on the healthy to ill spectrum and vary within individuals across mental states or in response to brain stimulation. In this work, we provide a novel measure of community strength, higher order clique conductance (HOCC), inspired by Benson 2016 that takes not only connections but maximal cliques of size k>2 (Fig 1c.) into account. Results from applied topology (Benson 2016; Horak 2009) show that maximal cliques and thus HOCC contain strictly as much or greater information than standard conductance. To estimate and compare HOCC across real data, we use recent advances in nonparametric bootstrap by Fasy et al. 2014 for topological quantities such as HOCC. Together, we provide a novel topological test statistic that is more powerful at detecting changes to community structure due to network changes.