Topology is an important component of the architecture of whole root systems. Unfortunately, most commonly applied indices used for characterizing topology are poorly correlated with one another and thus reflect different aspects of topology. In order to understand better how different methods of characterizing topology vary, this paper presents an exploration of several different methods for assigning order within branched root systems on the basis of (a) developmental (centrifugal) vs. functional (centripetal) ordering sequences and (b) whether orders are assigned to individual links or groups of adjacent links (segments). For each ordering system, patterns of scaling in relation to various aspects of link and segment size are explored using regression analyses. Segment-based ordering systems resulted in better fits for simple scaling relationships with size, but these patterns varied between developmental vs. functional ordering as well as the different size metrics examined. The functional (centripetal), link-based ordering system showed complex, non-linear scaling in relation to numbers of links per order. Using a simple simulation model of root growth, it is demonstrated that this method of characterizing root topology in relation to root size might be a more powerful tool for characterizing root system architecture than in the use of simple, single-index characterizations of topology.