Scaling laws in emotion-associated words and corresponding network topology

We investigated whether scaling laws were present in the appearance-frequency distribution of emotion-associated words and determined whether the network constructed from those words had small-world or scale-free properties. Over 1,400 participants were asked to write down the first single noun that came to mind in response to nine emotional cue words, resulting in a total of 12,556 responses. We identified Zipf’s law in the distribution of the data, as the slopes of the regression lines reached approximately −1.0 in the appearance frequencies for each emotional cue word. This suggested that the emotion-associated words had a clear regularity, were not randomly generated, were scale-invariant, and were influenced by unification/diversification forces. Thus, we predicted that the emotional intensity of the words might play an important role for a Zipf’s law. Moreover, we also found that the 1-mode network of emotion-associated words clearly had small-world properties in terms of the network topologies of clustering, average distance, and small-worldness value, indicating that all nodes (words) were highly interconnected with each other and were only a few short steps apart. Furthermore, the data suggested the possibility of a scale-free property. Interestingly, we were able to identify hub words with neutral emotional content, such as ‘dog’, ‘woman’, and ‘face’, indicating that these neutral words might be an intermediary between words with conflicting emotional valence. Additionally, efficiency and optimal navigation in terms of complex networks were discussed.