Relational network

A network is a type of structure like a tree, except that where a tree can only branch in one direction, a network branches into both directions -- so you can have paths that first branch and then come together. If we draw a diagram of a particular linguistic structure, parts of it look something like a net which would be used for fishing, although a good fishing net is a very perfect form of network in terms of mathematic structure. This we don't find. A relational network consists of lines and nodes, each node being a point at which lines intersect.

Comments
The notation system used for relational networks is an adaptation of the network notation developed by Halliday.

This network model is justified and was arrived at by analyzing relationships among linguistic units. Starting with the traditional assumption that a lexical item (likewise morpheme, phoneme) is a unit of some kind, an object or symbol or combination of symbols, we analyze its relationships to other units to which it is related. For example, morphemes are somehow related to elements of phonological expression on the one hand and to elements of conceptual information on the other. They are usually represented as symbols -- for example, 'boy', and these symbols represent their phonological (or graphic) realizations. Obviously, they are therefore related to the elements of their phonological realization and have to access them for production of speech.

These relationships can be represented as connections, the minimum requirement for any kind of relationship. Of course, positing connections leads inevitably to the need to posit nodes -- the points connected. A morpheme also 'has' higher-level properties -- grammatical and lexical or semantic -- and if we ponder what the meaning of 'has' is here, it is that the morpheme is connected to such properties. So we have further connections.

After the relationships of the morpheme to other elements -- phonological, grammatical, etc, are thus plotted, the symbol that has been representing it can be removed from the resulting diagrams with no loss of information. Whatever information it can be considered to represent is now already represented in the depiction of its relationships. This is especially clear in the case of the morpheme, since the symbol was just representing the components of its phonological representation, but these are now directly represented by connections.

Similarly, what do phonological symbols represent? They are just abbreviated notations for type and manner of articulation; so they have connections to those phonological properties, and after such connections are plotted, these symbols too are superfluous.

A similar line of reasoning applies to all the other linguistic units for which symbols have been used. They turn out to be just abbreviations for sets of connections.

Following this procedure, every unit of phonology and lexicon can be seen to be what it is by virtue of what its relationships are, and so can be seen as just the point in the system which has those relationships. And it appears that semantic and conceptual relationships can likewise be handled as relationships, with no units.

Upon removal of the symbols from the structure, the result is a network of relationships -- not symbols and relationships, just relationships, represented as interconnections among nodes. For what do the usual symbols for morphemes, for example boy, consist of? They are (spoken or written) expressions. But in the network representation the actual expression is already provided by the downward connections to elements of the phonological system, so there is no need to have a symbol within the system in addition.

Nevertheless, relational network diagrams would be hard to read without labels, so labels are used. But they're placed off to the side, because they're there only for the convenience of the viewer and are not part of the linguistic system.