This paper examines the implications of the association patterns in our understanding of the mental lexicon. By applying the principles of graph theory to word association data, we intend to explore which measures tap better into lexical knowledge. To that end, we had different groups of English as Foreign language learners complete a lexical fluency task. Based on these empirical data, a study was undertaken on the corresponding lexical availability graph (LAG). It is observed that the aggregation (mentioned through human coding) of all lexical tokens on a given topic allows the emergence of some lexical-semantic patterns. The most important one is the existence of some key terms, featuring both high centrality in the sense of network theory and high availability in the LAG, which define a hub of related terms. These communities of words, each one organized around an anchor term, or most central word, are nicely apprehended by a well-known network metric called modularity. Interestingly enough, each module seems to describe a conceptual class, showing that the collective lexicon, at least as approximated by LA Graphs, is organised and traversed by semantic mechanisms or associations via hyponymy or hiperonymy, for instance. Another empirical observation is that these conceptual hubs can be appended, resulting in high diameters compared to same-sized random graphs; even so it seems that the small-world hypothesis holds in LA Graphs, as in other social and natural networks.