Schur, E. (2007). Insights into the Structure of L1 and L2 Vocabulary Networks: Intimations of Small Worlds. In H. Daller, J. Milton, & J. Treffers-Daller (Eds.), Modelling and Assessing Vocabulary Knowledge (pp. 182-204). Cambridge: Cambridge University Press.
https://doi.org/10.1017/CBO9780511667268.013

has been cited by the following article:

• TITLE: A Note on Densities of the L2 Mental Lexicon Network

  AUTHORS: Yusuke Higuchi, Rumi Takahashi, Mikihiro Tanaka

  KEYWORDS: Mental Lexicon, Random Graph, Density, Complex Network, Second Language, Mathematical Modelling

  JOURNAL NAME: Open Journal of Modern Linguistics, Vol.9 No.6, December 4, 2019

  ABSTRACT: In this note, we discuss a supplementary explanation about works of Takahashi and Tanaka, which are a kind of replication study of Wilks & Meara (2002), where they discuss the structure of learners’ mental lexicon network from the viewpoint of psycholinguistics. Here we mainly discuss some mathematical structures which support their studies latently. Using some simple random graph techniques, we propose that the role of “densities” is important and useful under some suitable assumptions. Then, we exhibit the effectiveness of our method by applying it to the data of experiments in Takahashi and Tanaka, where some inequalities obtained mathematically help us to investigate some of the aspects of the L2 mental lexicon network. Mathematical proofs and detailed discussion are collected in the final section, in which we give also mathematical interpretation on some models which were shown by computer simulations in previous works.