The HEOM is a system of equations that contain, in principle, an infinite number of auxilary density operators (ADOs) possessing all the information about the system-bath correlations. As the name suggests, one can think of these coupled equations as being members of a hierarchical network. This structure however must of course be truncated for practical implementation. There have been a number of procedures implemented for achieving this including various decomposition techniques, basis set optimization, tensor network analysis and projection techniques. Other studies have focused on altering the topology of the hierarchy to tailor it to more complicated baths. In this work, we consider the importance of different auxilary density operators within a hierarchy by explicitly considering the flow of information through the elements of the hierarchy. This gives insight into which ADOs are fundamentally more important to the dynamics for a specific bath and paves the way for an alternative robust truncation procedure.