Typically, pieces of information in an interface are presented in a hierarchy. One example is the desktop metaphor. On a desktop typically multiple windows and icons reside in an overlapping manner. Icons can also reside in windows which in turn can be transformed into icons. Thus, the presentation hierarchy of the desktop metaphor consists of three levels. Icons are at the first level, which reside in windows at the second level, and which in turn reside in the desktop at the third level.
According to this model, the presentation hierarchy can be described
by node-link diagrams (Figure 
). In this model, nodes
correspond to visual presentations (e.g. icon, window, desktop, etc.)
of an entity in an interface. Links indicate either a visual
transformation (1:1) or a containment (M:1) relation. Links of type
1:1 indicate a visual transformation, where a node instance is
visually represented as another node instance in the presentation
hierarchy. For example, in Figure a window node instance
can be transformed into an icon node instance. On the other hand,
links of type M:1 indicate that multiple node instances are contained
in a composite node instance in the presentation hierarchy. For
example, in Figure multiple icon node instances are
contained in a window node instance.
Each node in the presentation hierarchy is associated with a set of
attributes and functions such as node capacity (C), screen space
requirement (S), layout function ( 
), representation function
( 
) and the information content (I). These attributes and
functions collectively describe the most important characteristics of
an interface, which will be used in the derivation of metrics and
factors.
Capacity (C) of a singular node is 1. Capacity of a composite node is the maximum quantity of node instances it can contain (e.g. number of icons in a window). Capacity of a node is typically bounded by the system resources (e.g. screen resolution, color palette, etc.). However, human capabilities (e.g. short-term memory, attention, visual system, etc.) also affect the usable capacity to a large degree.
Screen space requirement (S) of a node determines the amount of screen space needed by its visual representation in pixels. While for some nodes it can have a constant value, in some interfaces it is best described by a function which allows their screen space requirements to be changed dynamically.
The layout function ( ) of a composite node determines how the
node instances it contains are organized within the composite node's
space. In the desktop example, windows can be organized on the
desktop in tiled and overlapped styles, among other styles. Layouts
can be static as well as dynamically controlled by the user, thus it
is best described by a function.
Each node in the presentation hierarchy is mapped onto the screen
through its representation function ( ). Representation
functions typically map some attributes of the piece of information
that it contains (I) onto the screen, which could be textual
(e.g. name), visual (e.g. color, texture, image) and spatial
(e.g. location), among others.
Links between nodes are also associated with attributes such as cost and footprint. The cost of a link corresponds to the amount of time/steps (mouse clicks, keystrokes, etc.) it takes the user to access information from one node instance to the other. For example, to access the window associated with an icon, the user has to find the corresponding icon and double-click to open. Typically, human capabilities also affect the access cost to a large degree.
The footprint of a link is a measure of how well the information in a lower-level node instance is presented in the visual representation of the higher-level composite node instance. In the desktop example, footprint of an icon-window link corresponds to how well the image of an icon presents the information the window contains helping the user in the recall process. It is assumed to be a number between 0 (low) and 1 (high).
Let's apply the presentation hierarchy model to the WebBook and Web Forager, the vtwm (a twm-clone virtual window manager) and the Elastic Windows interfaces.