Both machines form a substantial part of a branch of the computer's genealogical tree.⁹   Only a decade later John van Neumann added his significant contribution, introducing the concept of a stored program. ¹⁰

I.2 Concepts

Although the machines invented by Turing and Post and Bush's Memex were mental constructs that only existed in their imaginations, today they are on the verge of becoming reality.

In the broad range and diversity of technological advances that are making this reality, we find hypertext.  Hyper means "extension into other dimensions", converting text  into  "a multidimensional space."

 Hypertext is defined as a non-linear text. The text is organized in such a way that inside the "text space" one can easily jump from topic to topic, reading without a predetermined sequence.

Hypertext is a tool for creating differently structured documents, which can be multi-level, cross-referenced and annotated in a way impossible to accomplish with a "DBASE" application or a standard word processor,

Although hypertext could he developed without a computer, with a number of documents and references organized around this concept, hypertext reaches its maximum potential when implemented in a computer system,

Since a computer provides the user with the possibility of moving through a tremendous number of texts, from one topic to another, rapid1y and with flexibility. This is so because the text for each topic can be stored in a special area of the computer's memory and can be easily accessed.

 Such movements are accomplished through what is called in hypertext terminology navigation tools, and the memory areas are referred to as labels, nodes, or markers.

The word node is derived from an approach to information management in which data has been stored in a network of nodes, which are interconnected through common relational space using software especially designed for a network. A node, in hypertext terminology, is usually a packet of data organized around a specified topic.

These concepts are found in nearly all the hypertexts available on the market today, although sometimes under other names or connotations specific to their creators. For example, in HyperCard a card is a node; in HyperPad a node is a pad; other hypertexts call a node a text segment, etc.

Actually, the concept of node is used in graph theory to represent points that may be interrelated, and the possible relations are represented by lines connecting the points. lf we were to express hypertext in a graph, it would be what is known as a complete graph.

Note that in figure 1, each node of the network affects the others through the lines, with no particular order or fixed direction. In other words, the lines represent possible navigation routes.

Figure 1. Complete Graph of 8 nodes.

Two other important elements of hypertext are finks and buttons, which are also called navigation tools. A link is a data item contained in or assigned to a node and connected to other nodes by construction. The position of link files in an internal structure depends exclusively on the design of the hypertext programmer.

A button is a link inserted in the text, highlighted in some manner un the screen, usually in contrast, thus allowing the user to position himself with the cursor in such a way that with one keystroke he can connect with associated nodes. In other words, a button is a visual link in a node.

The idea of hypertext is to break down a network of nodes into all of its possible trees or all possible trajectories that cover all the nodes of the network in function of predefined navigational elements. These possible routes of the user are trees, understood as the path through which two nodes are joined in a graph, since "in a graph two or more nodes are joined by only one path.¹¹

Returning to the complete graph in figure 1, and presupposing one or more links in common with all the nodes, 23 possible routes are generated along which the user can navigate.

Figure 2.  Eight node trees.

Graph theory provides a series of concepts and terms related to hypertext, especially navigation. Frank Harary, for example, defines a walk of graph G as an alternate sequence of points and fines, v0,  v1 , v2,...,vn which begin and end with points in which each line touches two points, the one, that immediately precedes it and the one that follows. A walk is closed if v0=v1 and open if this is not the case. A trail is a walk in which all lines are different .  A path is a walk in which all the points are different.