Skip to main content
SpringerLink
Log in

Complex Networks of Words in Fables

  • Chapter
  • First Online:
Maths Meets Myths: Quantitative Approaches to Ancient Narratives

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

In this chapter we give an overview of the application of complex network theory to quantify some properties of language. Our study is based on two fables in Ukrainian, Mykyta the Fox and Abu-Kasym’s slippers. It consists of two parts: the analysis of frequency-rank distributions of words and the application of complex network theory. The first part shows that the text sizes are sufficiently large to observe statistical properties. This supports their selection for the analysis of typical properties of the language networks in the second part of the chapter. In describing language as a complex network, while words are usually associated with nodes, there is more variability in the choice of links and different representations result in different networks. Here, we examine a number of such representations of the language network and perform a comparative analysis of their characteristics. Our results suggest that, irrespective of link representation, the Ukrainian language network used in the selected fables is a strongly correlated, scale-free, small world. We discuss how such empirical approaches may help to form a useful basis for a theoretical description of language evolution and how they may be used in analyses of other textual narratives.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The access to the electronic versions of these texts was through the most complete internet library of Ukrainian poetry, http://poetyka.uazone.net/.

  2. 2.

    The formation of a sentence may be considered (Thurner et al. 2015) as an example of a history-dependent process that becomes more constrained as it unfolds (Corominas-Murtra et al. 2015). Recently it has been demonstrated that stochastic processes of this kind necessarily lead to Zipf’s law too (Thurner et al. 2015; Corominas-Murtra et al. 2015).

  3. 3.

    For different network representations (different spaces) we use the nomenclature originally introduced in the context of transportation networks (Sienkiewicz and Hołyst 2005; von Ferber et al. 2007, 2009).

  4. 4.

    The British National Corpus is a collection of samples of written and spoken language from a wide range of sources, designed to represent a wide cross-section of British English from the late twentieth century, http://www.natcorp.ox.ac.uk/.

References

  • Albert, R., & Barabási, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97. doi:10.1103/RevModPhys.74.47.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Albert, R., Jeong, H., & Barabási, A.-L. (1999). Diameter of the World-Wide Web. Nature, 401, 130–131. doi:10.1038/43601.

    Article  ADS  Google Scholar 

  • Barceló-Coblijn, L., Corominas-Murtra, B., & Gomila, A. (2012). Syntactic trees and small-world networks: Syntactic development as a dynamical process. Adaptive Behavior, 20(6), 427. doi:10.1177/1059712312455439.

    Article  Google Scholar 

  • Borge-Holthoefer, J., & Arenas, A. (2010). Semantic networks: Structure and dynamics. Entropy, 12, 1264–1302. doi:10.3390/e12051264.

    Article  ADS  MATH  Google Scholar 

  • Bornholdt, S., & Schuster, H. (Eds.). (2003). Handbooks of graphs and networks. Weinheim: Wiley.

    Google Scholar 

  • Caldeira, S. M. G., Petit Lobão, T. C., Andrade, R. F. S., Neme, A., & Miranda, J. G. V. (2006). The network of concepts in written texts. European Physical Journal B: Condensed Matter and Complex Systems, 49, 523–529. doi:10.1140/epjb/e2006-00091-3.

    Article  ADS  Google Scholar 

  • Condon, E. U. (1928). Statistics of vocabulary. Science, 67, 300. doi:10.1126/science.67.1733.300.

    Article  ADS  Google Scholar 

  • Corominas-Murtra, B., Hanel, R., & Thurner, S. (2015). Understanding scaling through history-dependent processes with collapsing sample space. Proceedings of the National Academy of Sciences of the United States of America, 112, 5348–5353. doi:10.1073/pnas.1420946112.

  • Corominas Murtra, B., Valverde, S., & Solé, R. V. (2007). Emergence of scale-free syntax networks. Preprint. arXiv:0709.4344.

    Google Scholar 

  • de Jesus Holanda, A., Torres Pisa, I., Kinouchi, O., Souto Martinez, A., & Seron Ruiz, E. E. (2004). Thesaurus as a complex network. Physica A, 344, 530–536. doi:10.1016/j.physa.2004.06.025.

    Article  ADS  Google Scholar 

  • Diestel, R. (2005). Graph theory (Graduate texts in mathematics). Heidelberg: Springer.

    Google Scholar 

  • Dorogovtsev, S. N., & Mendes, J. F. F. (2001). Language as an evolving word web. Proceedings of the Royal Society B, 268, 2603–2606. doi:10.1098/rspb.2001.1824.

  • Dorogovtsev, S. N., & Mendes, J. F. F. (2003). Evolution of networks. Oxford: Oxford University Press.

    Book  MATH  Google Scholar 

  • Estoup, J. B. (1916). Gammes stenographiques. Paris: Institut Stenographique de France.

    Google Scholar 

  • Ferrer i Cancho, R. (2005). The variation of Zipf’s law in human language. European Physical Journal B: Condensed Matter and Complex Systems, 44, 249–257. doi:10.1140/epjb/e2005-00121-8.

    Article  ADS  Google Scholar 

  • Ferrer i Cancho, R., Riordan, O., & Bollobás, B. (2005). The consequences of Zipf’s law for syntax and symbolic reference. Proceedings of the Royal Society B, 272, 561–565. doi:10.1098/rspb.2004.2957.

  • Ferrer i Cancho, R., & Solé, R.V. (2001a). Two regimes in the frequency of words and the origin of complex lexicons: Zipf’s law revisited. Journal of Quantitative Linguistics, 8, 165–173. doi:1076/jqul.8.3.165.4101.

  • Ferrer i Cancho, R., & Solé, R. V. (2001b). The small world of human language. Proceedings of The Royal Society of London. Series B, Biological Sciences, 268, 2261–2265. doi:10.1098/rspb.2001.1800.

  • Ferrer i Cancho, R., Solé, R. V., & Köhler, R. (2004). Patterns in syntactic dependency networks. Physical Review E, 69, 051915. doi:10.1103/PhysRevE.69.051915.

  • Holovatch, Yu., & Palchykov, V. (2007). Mykyta the Fox and networks of language. Journal of Physical Studies, 11, 22–33 (in Ukrainian).

    ADS  Google Scholar 

  • Kanter, I., & Kessler, D. A. (1995). Markov processes: Linguistics and Zipf’s law. Physical Review Letters, 74, 4559–4562. doi:10.1103/PhysRevLett.74.4559.

    Article  ADS  Google Scholar 

  • Li, W. (1992). Random texts exhibit Zipf’s-law-like word frequency distribution. IEEE Transactions on Information Theory, 38, 1842–1845. doi:10.1109/18.165464.

    Article  Google Scholar 

  • Masucci, A. P., & Rodgers, G. J. (2006). Network properties of written human language. Physical Review E, 74, 026102. doi:10.1103/PhysRevE.74.026102.

    Article  ADS  Google Scholar 

  • Milgram, S. (1967). The small-world problem. Psychology Today, 2, 61–67.

    MathSciNet  Google Scholar 

  • Montemuro, M. A. (2001). Beyond the Zipf-Mandelbrot law in quantitative linguistics. Physica A, 300, 567–578. doi:10.1016/S0378-4371(01)00355-7.

    Article  ADS  MATH  Google Scholar 

  • Motter, A. E., de Moura, A. P. S., Lai, Y.-C., & Dasgupta, P. (2002). Topology of the conceptual network of language. Physical Review E, 65, 065102(R). doi:10.1103/PhysRevE.65.065102.

  • Newman, M. E. J. (2010). Networks: An introduction. Oxford: Oxford University Press.

    Book  MATH  Google Scholar 

  • Newman, M. E. J. (2012). Communities, modules and large-scale structure in networks. Nature Physics, 8, 25–31. doi:10.1038/nphys2162.

    Article  ADS  Google Scholar 

  • Nowak, M. A., & Krakauer, D. C. (1999). The evolution of language. Proceedings of the National Academy of Sciences of the United States of America, 96, 8028–8033. doi:10.1073/pnas.96.14.8028.

  • Petersen, A. M., Tenenbaum, J. N., Havlin, S., Stanley, H. E., & Perc, M. (2012). Languages cool as they expand: Allometric scaling and the decreasing need for new words. Scientific Reports, 2, 943. doi:10.1038/srep00943.

    ADS  Google Scholar 

  • Sienkiewicz, J., & HoÅ‚yst, J. A. (2005). Statistical analysis of 22 public transport networks in Poland. Physical Review E, 72, 046127. doi:10.1103/PhysRevE.72.046127.

    Article  ADS  Google Scholar 

  • Sigman, M., & Cecchi, G. A. (2002). Global organization of the Wordnet lexicon. Proceedings of the National Academy of Sciences of the United States of America, 99, 1742. doi:10.1073/pnas.022341799.

    Article  ADS  Google Scholar 

  • Simon, H. A. (1955). On a class of skew distribution functions. Biometrica, 44, 425–440. doi:10.1093/biomet/42.3-4.425.

    Article  MathSciNet  MATH  Google Scholar 

  • Solé, R. (2005). Syntax for free? Nature, 434, 289. doi:10.1038/434289a.

    Article  ADS  Google Scholar 

  • Solé, R. V., Corominas-Murtra, B., Valverde, S., & Steels, L. (2010). Language networks: Their structure, function, and evolution. Complexity, 15(6), 20. doi:10.1002/cplx.20305.

    Article  Google Scholar 

  • Solé, R. V., & Seoane, L. F. (2014). Ambiguity in language networks. The Linguistic Review, 32(1), 5–35. doi:10.1515/tlr-2014-0014.

    Google Scholar 

  • Thurner, S., Hanel, R., Liu, B., & Corominas-Murtra, B. (2015). Understanding Zipf’s law of word frequencies through sample-space collapse in sentence formation. Journal of the Royal Society Interface, 12, 20150330. doi:10.1098/rsif.2015.0330.

    Article  Google Scholar 

  • von Ferber, C., Holovatch, T., Holovatch, Yu., & Palchykov, V. (2007). Network harness: Metropolis public transport. Physica A, 380, 585–591. doi:10.1016/j.physa.2007.02.101.

    Article  ADS  Google Scholar 

  • von Ferber, C., Holovatch, T., Holovatch, Yu., & Palchykov, V. (2009). Public transport networks: Empirical analysis and modeling. European Physical Journal B, 68, 261–275. doi:10.1140/epjb/e2009-00090-x.

    Article  ADS  Google Scholar 

  • Watts, D. J. (1999). Small words. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Zhou, S., Hu, G., Zhang, Z., & Guan, J. (2008). An empirical study of Chinese language networks. Physica A, 387, 3039–3047. doi:10.1016/j.physa.2008.01.024.

    Article  ADS  Google Scholar 

  • Zipf, G. K. (1935). The psycho-biology of language. Boston: Houghton-Mifflin.

    Google Scholar 

  • Zipf, G. K. (1949). Human behaviour and the principle of least effort. An introduction to human ecology (1st ed.). Cambridge: Addison-Wesley (Hafner reprint, New York, 1972).

    Google Scholar 

Download references

Acknowledgements

It is our pleasure to thank the Editors of this book Ralph Kenna, Máirín MacCarron, and Pádraig MacCarron for their invitation to contribute and for their help and discussions during preparation of the manuscript. Yu.H. acknowledges useful discussions with Bernat Corominas-Murtra. This work was supported in part by the 7th FP, IRSES projects No. 295302 Statistical Physics in Diverse Realizations (SPIDER), No. 612707 Dynamics of and in Complex Systems (DIONICOS), by the COST Action TD1210 Analyzing the dynamics of information and knowledge landscapes (KNOWSCAPE) and by SNSF project No. 147609 Crowdsourced conceptualization of complex scientific knowledge and discovery of discoveries.

Author information

Authors and Affiliations

  1. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 79011, Lviv, Ukraine

    Yurij Holovatch & Vasyl Palchykov

  2. Lorentz Institute for Theoretical Physics, Leiden University, 2300 RA, Leiden, The Netherlands

    Vasyl Palchykov

Authors
  1. Yurij Holovatch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vasyl Palchykov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vasyl Palchykov .

Editor information

Editors and Affiliations

  1. Applied Mathematics Research Centre, Coventry University, Coventry, United Kingdom

    Ralph Kenna

  2. Department of History, University of Sheffield, Sheffield, United Kingdom

    Máirín MacCarron

  3. Department of Experimental Psychology, University of Oxford, Oxford, United Kingdom

    Pádraig MacCarron

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Holovatch, Y., Palchykov, V. (2017). Complex Networks of Words in Fables. In: Kenna, R., MacCarron, M., MacCarron, P. (eds) Maths Meets Myths: Quantitative Approaches to Ancient Narratives. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-39445-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation