This article presents a novel approach for understanding information exchange efficiency and its decay across hierarchies of modularity, from local to global, of the structural human brain connectome. Magnetic resonance imaging techniques have allowed us to study the human brain connectivity as a graph, which can then be analyzed using a graph-theoretical approach. Collectively termed brain connectomics, these sophisticated mathematical techniques have revealed that the brain connectome, like many networks, is highly modular and brain regions can thus be organized into communities or modules. Here, using tractography-informed structural connectomes from 46 normal healthy human subjects, we constructed the hierarchical modularity of the structural connectome using bifurcating dendrograms. Moving from fine to coarse (i.e., local to global) up the connectome's hierarchy, we computed the rate of decay of a new metric that hierarchically preferentially weighs the information exchange between two nodes in the same module. By computing "embeddedness"-the ratio between nodal efficiency and this decay rate, one could thus probe the relative scale-invariant information exchange efficiency of the human brain. Results suggest that regions that exhibit high embeddedness are those that comprise the limbic system, the default mode network, and the subcortical nuclei. This supports the presence of near-decomposability overall yet relative embeddedness in select areas of the brain. The areas we identified as highly embedded are varied in function but are arguably linked in the evolutionary role they play in memory, emotion and behavior.