The paper proposes a mathematical method of defining dependency and constituency provided linguistic criteria to characterize the acceptable fragments of an utterance have been put forward. The method can be used to define syntactic structures of sentences, as well as discourse structures for texts, or even morphematic structures for words. Our methodology leads us to put forward the notion of connection, simpler than dependency, and to propose various representations which are not necessarily trees. We also study criteria to refine and hierarchize a connection structure in order to obtain a tree.