This paper investigates the relation of syntax and communicative functions. We contrasted Dependency Grammar (DG) that sees syntax as autonomous and independent of its possible communicative uses with Construction Grammar (CxG) that maintains that the building blocks of language are stored form-meaning pairings, including phrasal patterns which may be associated with particular communicative or discourse functions. We constructed two treebanks of Hebrew, of parental speech and of young children's speech, parsing the sentences for DG and coding them for the communicative function of the utterances. The communicative-syntactic system is modeled as a bipartite network of verb-direct object (VO) combinations and of communicative functions (CF). DG predicts that VO-CF matching be scale-free, whereas CxG predicts that the matching is one-to-one. Next, we analyzed the degree of assortativity of the VO-CF bipartite network. We calculated a Pearson's correlation coefficient between the degrees of all pairs of connected nodes, predicting a positive assortativity on CxG and a negative one, on DG. The results do not support the concept of holistic constructions fusing syntactic structures and communicative functions. Instead, the communicative-syntactic system is a complex system with sub-systems mapping onto one another.