I Grammar structures

1.1 Overview of the grammar structure

The cluster grammar introduces graph networks, which we refer to as the cluster graphs, which have the directed graph structure instead of the trees used in classical grammar theory such as the Generative Grammar. The cluster graphs consist of two graphs: the morpheme graph which consists of the whole morphemes of a language and the signifié graph which consists of the signifiés that correspond to the morphemes.
The morpheme graph is a directed graph which consists of the morphemes as its nodes and the edges connecting them. The signifié graph has signifiés which correspond to the morphemes which are the nodes of the morpheme graph. The correspondence between these two graphs is not the signification as the morpheme graph only deals with morphemes, not signifiants. Morphemes that correspond to several different signifiés are distinguished from each other. Because signifiants are only signs and the structure of the graph is deeply concerned with the sentence generation process, the nodes of such a graph should be morphemes.
The directed edges of the morpheme graph are determined by the grammatic order of the morphemes, and vice versa. The following graph a and graph b are the examples of the morpheme graph. The arrows show the order of the enumeration of the morphemes. (q.v. 1.2)