[PS-1.3] Hypernetwork Analysis of Language Networks and Its Implication for Brain Networks

Zhang, M. 1 , Kim, J. S. 2 & Nam, J. . 1

1 Sangmoon High School, Seoul 137-060, Republic of Korea
2 Seoul National University, Seoul 151-742, Republic of Korea

Previous studies show that brain networks follow power laws. Language networks are also known to follow power laws. Language is generated and interpreted by the brain. These suggest that we can get insight into brain networks from studying language networks and vice versa. Here we propose to use the hypernetwork model for studying language use and its implications for brain architecture. Formally, a hypernetwork is a weighted hypergraph and we define a k-hypernetwork as a collection of k-hyperedges, where each k-hyperedge consists of a set of k vertices and a weight value denoting the edge strength. In language modeling, each k-hyperedge consists of k consecutive words in a sentence and, thus, a k-hypernetwork represents the k-gram distribution of a language corpus. We have analyzed the k-hypernetwork structures of TV drama dialogues, i.e. the full episodes of Friends run for 10 years, and found they follow the power law for k = 1 or larger. In contrast, we did not observe the power law in the k-hypernetworks constructed by random hyperedge sampling from the uniform distribution of the same vocabulary. We also compared the property of the k-hypernetworks of the drama dialogues with that of the news articles. Their unigram distributions, i.e. 1-hypernetworks, were the same while their higher-order k-gram distributions, i.e. k-hypernetworks for k = 2 or higher, were significantly different. In particular, drama dialogues have larger coefficients for the power, meaning that they have more extreme rich-get-richer properties than the news articles. We conclude that the hypernetwork models are effective tools for capturing the higher-order probabilistic properties of language use. It remains to study how the hypernetworks ?evolve? as new language data are observed in sequence as in language acquisition. This may shed light on organizational processes of the brain networks involved with cognitive development of language.