Toward a model of language acquisition threshold

We demonstrate how the paradigm of complex networks can be used to model some aspects of the process of second language acquisition. When learning a new language, knowledge of 3000-4000 of the most frequent words appears to be a significant threshold, necessary to transfer reading skills from L1 to L2(1). We show that this threshold corresponds to the transition from Zipf's law to a non-Zipfian regime in the rank-frequency plot of words of the English language. Using a large dictionary, we then construct a graph representing this dictionary, and study topological properties of subgraphs generated by the k most frequent words of the language. The clustering coefficient of these subgraphs reaches a minimum in the same place as the crossover point in the rank-frequency plot. We conjecture that the coincidence of all these thresholds may indicate a change in the language structure, which occurs when the vocabulary size reaches about 3000-4000 words.