This paper presents a computational model of the incremental construction of an associative network from a corpus. It is aimed at modeling the development of the human semantic memory. It is not based on a vector representation, which does not well reproduce the asymmetrical property of word similarity, but rather on a network representation. Compared to Latent Semantic Analysis, it is incremental which is cognitively more plausible. It is also an attempt to take into account higher-order co-occurrences in the construction of word similarities. This model was compared to children association norms. A good correlation as well as a similar gradient of similarity were found