Halliday (2008: 66):
The vertical axis of the network is unordered; systems are arranged so as to make the two-dimensional representation of the wiring as simple as possible. But the horizontal axis is ordered from left to right on a scale of delicacy, or refinement in detail (referred to in computational grammars as “granularity”). Here the ordering is determined by the interrelations among the various systems, irrespective of how their terms are realised in structure. This is a fundamental consideration: one of the reasons for making the underlying representation paradigmatic was in order to free it from constraints of structure, so that every feature could be located according to its relationship with other features. In other words, describing something, and relating it to everything else (to its agnates), which in a description based on structure are two distinct operations, in a systemic grammar are one and the same operation. Each feature is described by being located in its paradigmatic context.