Abstract
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.
References
Adamic L (2011) Unzipping Zipf’s law. Nature 474:164–165. doi:10.1038/474164a
Albert R, Jeong H, Barabási A-L (1999) Internet: diameter of the world-wide web. Nature 401:130–131
Alonso-Arbiol I, Shaver PR, Fraley RC, Oronoz B, Unzurrunzaga E, Urizar R (2006) Structure of the Basque emotion lexicon. Cognit Emot 20:836–865. doi:10.1080/02699930500405469
Baek SK, Bernhardsson S, Minnhagen P (2011) Zipf’s law unzipped. New J Phys 13:043004. doi:10.1088/1367-2630/13/4/043004
Balasubrahmanyan VK, Naranan S (1996) Quantitative linguistics and complex system studies. J Quant Linguist 3:177–228. doi:10.1080/09296179608599629
Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
Baronchelli A, Ferrer-i-Cancho R, Pastor-Satorras R, Chater N, Christiansen MH (2013) Networks in cognitive science. Trends Cogn Sci 17:348–360. doi:10.1016/j.tics.2013.04.010
Bastian M, Heymann S, Jacomy M (2009) Gephi: an open source software for exploring and manipulating networks. Int AAAI Conf Weblogs Soc Media 8:361–362
Batagelj V, Mrvar A (2004) Pajek—analysis and visualization of large networks. In: Jünger M, Mutzel P (eds) Graph drawing software. Springer, Berlin, pp 77–104
Beckage N, Smith L, Hills T (2011) Small worlds and semantic network growth in typical and late talkers. PLoS ONE 6:e19348. doi:10.1371/journal.pone.0019348
Borgatti SP, Everett MG (1997) Network analysis of 2-mode data. Soc Netw 19:243–269
Borgatti SP, Everett MG, Freeman LC (2002) Ucinet 6 for windows. Analytic Technologies, Harvard
Borsboom D, Cramer AO, Schmittmann VD, Epskamp S, Waldorp LJ (2011) The small world of psychopathology. PLoS ONE 6:e27407. doi:10.1371/journal.pone.0027407
Bower GH (1981) Mood and memory. Am Psychol 36:129–148
Church T, Katigbak MS, Reyes JAS, Jensen SM (1998) Language and organisation of Filipino emotion concepts: comparing emotion concepts and dimensions across cultures. Cognit Emot 12:63–92. doi:10.1080/026999398379781
Clutton-Brock TH, Harvey PH (1980) Primates, brain and ecology. J Zool 190:309–323
Collins AM, Loftus EF (1975) A spreading-activation theory of semantic processing. Psychol Rev 82:407–428
Coronges KA, Stacy AW, Valente TW (2007) Structural comparison of cognitive associative networks in two populations. J Appl Soc Psychol 37:2097–2129. doi:10.1111/j.1559-1816.2007.00253.x
de Castro R, Grossman JW (1999) Famous trails to Paul Erdős. Math Intell 21:51–53
De Deyne S, Storms G (2008) Word associations: norms for 1,424 Dutch words in a continuous task. Behav Res Methods 40:198–205. doi:10.3758/BRM.40.1.198
Edwards AM, Freeman MP, Breed GA, Jonsen ID (2012) Incorrect likelihood methods were used to infer scaling laws of marine predator search behaviour. PLoS ONE 7:e45174. doi:10.1371/journal.pone.0045174
Ekman P (1992) An argument for basic emotions. Cognit Emot 6:169–200
Ekman P, Friesen WV (1971) Constants across cultures in the face and emotion. J Pers Soc Psychol 17:124–129
Ekman P, Friesen WV (1975) Unmasking the face. Prentice Hall, Englewood
Ferreira AAA, Corso G, Piuvezam G, Alves MSCF (2006) A scale-free network of evoked words. Braz J Phys 36:755–758. doi:10.1590/S0103-97332006000500032
Ferrer-i-Cancho R (2005) Decoding least effort and scaling in signal frequency distributions. Phys A 345:275–284. doi:10.1016/j.physa.2004.06.158
Ferrer-i-Cancho R, Solé RV (2001a) Two regimes in the frequency of words and the origins of complex lexicons: Zipf’s law revisited. J Quant Linguist 8:165–173. doi:10.1076/jqul.8.3.165.4101
Ferrer-i-Cancho R, Solé RV (2001b) The small world of human language. Proc R Soc Lond B Biol Sci 268:2261–2265. doi:10.1098/rspb.2001.1800
Ferrer-i-Cancho R, Solé RV (2003) Least effort and the origins of scaling in human language. Proc Natl Acad Sci USA 100:788–791. doi:10.1073/pnas.0335980100
Galati D, Sini B, Tinti C, Testa S (2008) The lexicon of emotion in the neo-Latin languages. Soc Sci Inf 47:205–220. doi:10.1177/0539018408089079
Harremoës P, Topsøe F (2005) Zipf’s law, hyperbolic distributions and entropy loss. Electron Notes Discrete Math 21:315–318
Hills TT, Maouene M, Maouene J, Sheya A, Smith L (2009) Longitudinal analysis of early semantic networks: preferential attachment or preferential acquisition? Psychol Sci 20:729–739. doi:10.1111/j.1467-9280.2009.02365.x
Hills TT, Kalff C, Wiener JM (2013) Adaptive Lévy processes and area-restricted search in human foraging. PLoS ONE 8:e60488. doi:10.1371/journal.pone.0060488
Humphries MD, Gurney K (2008) Network ‘small-world-ness’: a quantitative method for determining canonical network equivalence. PLoS ONE 3:e0002051. doi:10.1371/journal.pone.0002051
Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási A-L (2000) The large-scale organization of metabolic networks. Nature 407:651–654
Ke J, Yao Y (2008) Analysing language development from a network approach. J Quant Linguist 15:70–99. doi:10.1080/09296170701794286
Knuth DE (1993) The Stanford GraphBase: a platform for combinatorial computing. Addison-Wesley, Reading
Latapy M, Magnien C, Del Vecchio N (2008) Basic notions for the analysis of large two-mode networks. Soc Netw 30:31–48. doi:10.1016/j.socnet.2007.04.006
Latora V, Marchiori M (2001) Efficient behaviour of small-world networks. Phys Rev Lett 87:198701. doi:10.1103/PhysRevLett.87.198701
Levenson RW (1999) The intrapersonal functions of emotion. Cognit Emot 13:481–504
Ludueña GA, Behzad MD, Gros C (2014) Exploration in free word association networks: models and experiment. Cogn Process 15:195–200. doi:10.1007/s10339-013-0590-0
Lundgren R, Olesen JM (2005) The dense and highly connected world of Greenland’s plants and their pollinators. Arct Antarct Alp Res 37:514–520. doi:10.1657/1523-0430(2005)037[0514:TDAHCW]2.0.CO;2
Marino L (1996) What can dolphins tell us about primate evolution? Evolu Anthropol 5:81–85
Mathias N, Gopal V (2001) Small worlds: how and why. Phys Rev E 63:021117. doi:10.1103/PhysRevE.63.021117
McCowan B, Hanser SF, Doyle LR (1999) Quantitative tools for comparing animal communication systems: information theory applied to bottlenose dolphin whistle repertoires. Ani Behav 57:409–419
Motter AE, de Moura APS, Lai Y-C, Dasgupta P (2002) Topology of the conceptual network of language. Phys Rev E 65:065102. doi:10.1103/PhysRevE.65.065102
Naranan S, Balasubrahmanyan V (1998) Models for power law relations in linguistics and information science. J Quant Linguist 5:35–61. doi:10.1080/09296179808590110
Nelson DL, McEvoy CL, Schreiber TA (2004) The University of South Florida free association, rhyme, and word fragment norms. Behav Res Methods Instrum Comput 36:402–407. doi:10.3758/BF03195588
Nelson DL, Dyrdal GM, Goodmon LB (2005) What is preexisting strength? Predicting free association probabilities, similarity ratings, and cued recall probabilities. Psychon Bull Rev 12:711–719. doi:10.3758/BF03196762
Nesse RM (1990) Evolutionary explanations of emotions. Human Nat 1:261–289
Neta M, Davis FC, Whalen PJ (2011) Valence resolution of ambiguous facial expressions using an emotional oddball task. Emotion 11:1425–1433. doi:10.1037/a0022993
Newman MEJ (2001) The structure of scientific collaboration networks. Proc Natl Acad Sci USA 98:404–409. doi:10.1073/pnas.98.2.404
Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256. doi:10.1137/S003614450342480
Newman MEJ (2004) Coauthorship networks and patterns of scientific collaboration. Proc Natl Acad Sci USA 101:5200–5205. doi:10.1073/pnas.0307545100
Newman MEJ (2006) Finding community structure in networks using the eigenvectors of matrices. Phys Rev E 74:036104. doi:10.1103/PhysRevE.74.036104
Niedenthal P, Auxiette C, Nugier A, Dalle N, Bonin P, Fayol M (2004) A prototype analysis of the French category “émotion”. Cognit Emot 18:289–312. doi:10.1080/02699930341000086
Öhman A (2008) Fear and anxiety: overlaps and dissociation. In: Lewis M, Haviland-Jones JM, Feldman-Barrett L (eds) Handbook of emotions, 3rd edn. Guilford Press, New York, pp 709–729
Petersen AM, Tenenbaum JN, Havlin S, Stanley HE, Perc M (2012) Languages cool as they expand: allometric scaling and the decreasing need for new words. Sci Rep 2:943. doi:10.1038/srep00943
Raphael B, Minkov C (1999) Abnormal grief. Curr Opin Psychiatry 12:99–102
Reisenzein R (2000) The subjective experience of surprise. In: Bless H, Forgas JP (eds) The message within: the role of subjective experience in social cognition and behavior. Psychology Press, Philadelphia, pp 262–279
Shaver PR, Schwartz J, Kirson D, O’Connor C (1987) Emotion knowledge: further exploration of a prototype approach. J Pers Soc Psychol 52:1061–1086
Shaver PR, Murdaya U, Fraley RC (2001) Structure of the Indonesian emotion lexicon. Asian J Soc Psychol 4:201–224. doi:10.1111/1467-839X.00086
Shiota MN, Keltner D (2005) What do emotion words represent? Psychol Inqui 16:32–37
Solé RV, Corominas-Murta B, Valverde S, Steels L (2010) Language networks: their structure, function, and evolution. Complexity 15:20–26. doi:10.1002/cplx.20305
Steyvers M, Tenenbaum JB (2005) The large-scale structure of semantic networks: statistical analyses and a model of semantic growth. Cognit Sci 29:41–78. doi:10.1207/s15516709cog2901_3
Thompson CP (1985) Memory for unique personal events: effect of pleasantness. Motiv Emot 9:277–289
Toivonen R, Kivelä K, Saramäki J, Viinikainen M, Vanhatalo M, Sams M (2012) Networks of emotion concepts. PLoS ONE 7:e28883. doi:10.1371/journal.pone.0028883
Tsonis AA, Schultz C, Tsonis PA (1997) Zipf’s law and the structure and evolution of languages. Complexity 2:12–13
Wagenaar WA (1986) My memory: a study of autobiographical memory over six years. Cognit Psychol 18:225–252
Wang B, Cao L, Suzuki H, Aihara K (2012) Safety-information-driven human mobility patterns with metapopulation epidemic dynamics. Sci Rep 2:887. doi:10.1038/srep00887
Wasserman S, Faust K (1994) Social networks analysis: methods and applications. Cambridge University Press, Oxford
Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442
Williams RJ, Berlow EL, Dunne JA, Barabási A-L, Martinez ND (2002) Two degrees of separation in complex food webs. Proc Natl Acad Sci USA 99:12913–12916. doi:10.1073/pnas.192448799
Zammuner VL (1998) Concepts of emotion: “Emotionness”, and dimensional ratings of Italian emotion words. Cognit Emot 12:243–272
Zanette D, Montemurro M (2005) Dynamics of text generation with realistic Zipf’s distribution. J Quant Linguist 12:29–40. doi:10.1080/09296170500055293
Zipf GK (1949) Human behavior and the principle of least effort. Addison-Wesley, Cambridge
Acknowledgments
This research was supported by the Ministry of Education, Culture, Sports, Science and Technology Grant-in-Aid for Challenging Exploratory Research, 24650140, 2012, awarded to the primary author. We are grateful to Toshio Shibata, Kunio Midzuno, Toru Tazumi, Takanobu Baba, Yosuke Tezuka, Kyoko Yamamoto, and Akemi Takehara for their assistance. We are also grateful to Guston Rankin, Mariko Shirai, and two anonymous reviewers for their extremely valuable comments.
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Takehara, T., Ochiai, F. & Suzuki, N. Scaling laws in emotion-associated words and corresponding network topology. Cogn Process 16, 151–163 (2015). https://doi.org/10.1007/s10339-014-0643-z
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DOI: https://doi.org/10.1007/s10339-014-0643-z