Language as a Small World Network

Small world networks are graphs, which integrate the properties of random graphs and lattice graphs [5]. Several real networks can be modeled with a help of small worlds [1, 2, 6, 8]. As shown in this paper a word web has small world structure too. We have shown, that different languages, such as Slovak and English, have similar small world properties. As our second goal, we built a graph on the basis of kernel lexicon words, in order to test the scaling results of Cancho and Sol¿ [6]. We speculate that the differences between calculated and measured exponents of connectivity distribution are due to the node aging.

[1]  Gerard Kempen,et al.  The lexicalization process in sentence production and naming: indirect election of words , 1983, Cognition.

[2]  Partha Dasgupta,et al.  Topology of the conceptual network of language. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[4]  Ricard V. Solé,et al.  Complexity and fragility in ecological networks , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[5]  G. Miller,et al.  How children learn words. , 1987, Scientific American.

[6]  Martin A. Nowak,et al.  The evolution of syntactic communication , 2000, Nature.

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  Roger S. Brown,et al.  The "Tip of the Tongue" Phenomenon , 1966 .

[9]  S. N. Dorogovtsev,et al.  Scaling properties of scale-free evolving networks: continuous approach. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[11]  David Caplan,et al.  Neurolinguistics and linguistic aphasiology , 1987 .

[12]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[13]  M. Grossman,et al.  Language: Structure, Processing, and Disorders , 1993 .

[14]  菅山 謙正,et al.  Word Grammar 理論の研究 , 2005 .

[15]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[16]  Suzanne Romaine.  Pidgin and Creole Languages , 1988 .

[17]  K. Forster,et al.  Lexical Access and Naming Time. , 1973 .

[18]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[19]  J. Nicolis,et al.  Chaos and information processing , 1991 .

[20]  Eörs Szathmáry,et al.  The Major Transitions in Evolution , 1997 .

[21]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[22]  D. Zanette.  Dynamics of rumor propagation on small-world networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[24]  Wentian Li,et al.  Random texts exhibit Zipf's-law-like word frequency distribution , 1992, IEEE Trans. Inf. Theory.

[25]  S N Dorogovtsev,et al.  Language as an evolving word web , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[26]  Ricard V. Solé,et al.  Two Regimes in the Frequency of Words and the Origins of Complex Lexicons: Zipf’s Law Revisited* , 2001, J. Quant. Linguistics.

[27]  M A Nowak,et al.  The evolution of language. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Gesine Reinert,et al.  Small worlds , 2001, Random Struct. Algorithms.

[29]  Mark Newman,et al.  Models of the Small World , 2000 .

[30]  Donald Favareau.  The Symbolic Species: The Co-evolution of Language and the Brain , 1998 .

[31]  S. Naranan,et al.  Quantitative Linguistics and Complex System Studies , 1996, J. Quant. Linguistics.

[32]  C. Habel,et al.  Language , 1931, NeuroImage.

[33]  Abraham Kaplan,et al.  An experimental study of ambiguity and context , 1955, Mech. Transl. Comput. Linguistics.

[34]  Susan Bowsfield.  The Symbolic Species: The Co-Evolution of Language and the Brain , 2004 .

[35]  Don L. Scarborough,et al.  Frequency and Repetition Effects in Lexical Memory. , 1977 .

[36]  Arnab Chatterjee,et al.  Small-world properties of the Indian railway network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Carson C. Chow,et al.  Small Worlds , 2000 .

[38]  Jose M. Montoya Ricard V. Sole,et al.  Small world patterns in food webs. , 2000, Journal of theoretical biology.

[39]  Ramon Ferrer i Cancho,et al.  The small world of human language , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[40]  George Kingsley Zipf,et al.  Human Behaviour and the Principle of Least Effort: an Introduction to Human Ecology , 2012 .

[41]  Yaacov Choueka,et al.  Disambiguation by short contexts , 1985, Comput. Humanit..

[42]  M. Newman.  Models of the Small World: A Review , 2000, cond-mat/0001118.

[43]  J. Montoya,et al.  Small world patterns in food webs. , 2002, Journal of theoretical biology.

[44]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[45]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[46]  Adrian Akmajian,et al.  Linguistics: An Introduction to Language and Communication , 1979 .