Small worlds and semantic network growth in typical and late talkers

Abstract

Network analysis has demonstrated that systems ranging from social networks to electric power grids often involve a small world structure-with local clustering but global ac cess. Critically, small world structure has also been shown to characterize adult human semantic networks. Moreover, the connectivity pattern of these mature networks is consistent with lexical growth processes in which children add new words to their vocabulary based on the structure of the language-learning environment. However, thus far, there is no direct evidence that a child's individual semantic network structure is associated with their early language learning. Here we show that, while typically developing children's early networks show small world structure as early as 15 months and with as few as 55 words, children with language delay (late talkers) have this structure to a smaller degree. This implicates a maladaptive bias in word acquisition for late talkers, potentially indicating a preference for "oddball" words. The findings provide the first evidence of a link between small-world connectivity and lexical development in individual children.

Figure 1. Random acquisition networks acquired from the learning environment show different structure from comparable Erdős Rényi (ER) random graphs.

When semantic relatedness was used to provide connections between words, ER networks showed less clustering and lower median in-degree than random acquisition networks even when matched for density, indicating that the language environment is more structured than its random equivalent. To generate samples of random acquisition graphs, we sampled 100 random sets of words equal in number to each child's vocabulary size. Edges in the random acquisition networks were based on the same co-occurrence data as was used to build the networks of individual children. This was then averaged to get a single set of network statistics representing random acquisition for a given child. ER networks were built to contain the same overall number of edges as the averaged random acquisition graph, with 100 repetitions at the level of the individual child. All pairs are significantly different (p<.0001) with dark grey representing the ER random graphs and light grey representing the random acquisition graphs.

Figure 2. Network graphs for two individual children.

The graph on the left is a typically developing (TD) child (17 mo, 40%) and the graph on the right is of an at-risk, late-talker (LT) (24 mo, 10%). The network of the TD child includes the 60 words in the child's productive vocabulary and the network of the at-risk LT child includes the 61 words in the child's productive vocabulary. The apparent visual differences in the networks are supported by the differences in the corresponding table, with the typical talker's network showing higher clustering coefficient and higher median in-degree, but lower geodesic distance, than the LT. These differences are consistent at both the individual and population level.

Figure 3. Ratios of differences relative to the child-matched random acquisition networks for both typical talkers (TD, dark gray) and late talkers (LT, light grey).

TD children show marginally significant (p = 0.0970) effects of greater median in-degree and LT children show significantly less (p<0.001) median in-degree than the random acquisition networks. While TD children have clustering coefficients indistinguishable from random acquisition, the late talkers have significantly less (p<0.001) clustering than their paired random acquisition networks. TDs have no significant difference between their paired random acquisition networks whereas LTs have a significantly higher (p = .0092) geodesic distance. Error bars indicate standard error.