AbstractThe goal of this paper is to establish a new approach with graph networks, which we refer to as the cluster grammar, as a computational linguistic grammar. The main content of this paper is the construction of the theory and the verification of its potential for application in computer science.We begin by introducing the graph networks, which we refer to as cluster graphs. The graphs are considered as the essential elements for the language ability. The innate abilities that we introduce in order to elucidate the acquisition of the language ability, generation and processing of sentences are given as graph theoretical algorithms. The theory includes a sort of verification problem as well as the Universal Grammar introduced by Chomsky, however the theory is intended to be applied for information technology where the given algorithms and methods can be developed further to have computers process languages with more developed data structure and more human.Contents:IntroductionGrammar StructureAcquisition of the Language Ability and Application for ComputerConclusion and further investigationReferences