Stratum

The stratum metric was designed to capture the linear ordering of a hyperdocument. Stratum represents how much or little choice the user has while browsing through a hyperdocument. The term stratum is taken from an analogous concepts in organizations. Some companies have a very rigid hierarchical organization. The president only talks to the vice-presidents, who only talk to the directors, and those only to their immediate assistants, etc. For an employee at the bottom of the hierarchy it is very hard, if not impossible, to reach the president without going through all the intermediaries. Other companies are much more flexible, and the interaction between bosses and employees is accomplished much more easily. Companies of the first type are said to be stratified while the others are not stratified.

In the same way, authors of hyperdocuments can either write in a very stratified or hierarchical way, with few cross-reference links between the nodes, or can be more liberal in the use of cross-reference links. The best way to organize a hyperdocument depends on the application, the author(s) and the readers. In a hierarchical document it is less likely to get lost, so a higher stratum suggests that readers are less likely to suffer from the "lost in hyperspace" syndrome. On the other hand, cross-reference links (representing lower-level employees talking to higher-level managers) are what makes hypertext different from hierarchically structured books. So stratum basically measures the amount of cross-referencing.

The definition of stratum is based on the distance matrix (without conversion).

The prestige of node i is Ai - Bi. The total prestige (sum of all prestiges) of a hyperdocument is always 0. Therefore we define the absolute prestige (or absolute stratum) of D as the sum of the absolute values of the prestige of each node.

The absolute prestige grows with the size of the hyperdocument. In order to normalize it we compare it to the prestige of a linear document of the same size.

The linear absolute prestige (LAP) of a hyperdocument with n nodes is the absolute prestige of a linear hyperdocument with n nodes.

The stratum of a hypertext is defined as its absolute prestige divided by its LAP.

The normalization in the stratum metric is rather arbitrary. One could equally well define a different normalization by dividing by the prestige of a balanced binary (or other) tree, by number of links, by lengths of paths or by whatever measure on the document structure one considers important for reading without getting lost. Also, normalization is questionable in general, since larger documents are always more difficult to read than small ones. So the size of the document should not simply be normalized out.