Graph theory is a branch of mathematics that is used to study networks. Recently, graph theoretic techniques have been embraced by the cognitive sciences, and used to study the developing lexicon, semantic memory, and first and second language organization (Carlson,et al., 2011, Kennet et al., 2011, Wilks & Meara, 2002, Zareva, 2007) Graph theory can give valuable insight into the underlying phonological structure of language. Studying phonological networks contributes to our understanding of how the mental lexicon develops, and results of experimental studies on lexical processing can be used to test whether the proposed network structure is plausible. The goal of this dissertation was to examine the organization of a lexicon of words from a storybook corpus in terms of phonological properties. This goal was achieved by using graph theory techniques.
Two networks were defined for graph theoretic analysis. Different metrics were used to define the edges for these two networks to model different organization of neighbors of the developing mental lexicon. Word types from storybooks frequently read to 2-4 year-old children were represented in both networks. Using graph theoretic techniques, degree centrality and betweenness centrality measures were calculated for both networks. Words that represented nodes of the network with high degree and high betweenness centrality were examined. Age of acquisition, word frequency, and measures of phonotactic probability were calculated for these prominent nodes in both networks. Comparisons of lexical and sublexical characteristics for words that represented high degree and high betweenness centrality nodes were made. Comparisons were also made between the general structures of both networks related to word categories (function and content) and morphological complexity.
Results of this dissertation indicate that the words (nodes) that hold prominent positions in these two differently-defined networks are not identical, nor are their connections. Differences were also evident in lexical and sublexical characteristics of words that represent prominent nodes within each network. The two networks also revealed different features in overall connections between words (nodes) and word types. Implications regarding how this reflects child language development is discussed