Behavior Research Methods

, Volume 50, Issue 1, pp 427–449 | Cite as

GraphCom: A multidimensional measure of graphic complexity applied to 131 written languages



We report a new multidimensional measure of visual complexity (GraphCom) that captures variability in the complexity of graphs within and across writing systems. We applied the measure to 131 written languages, allowing comparisons of complexity and providing a basis for empirical testing of GraphCom. The measure includes four dimensions whose value in capturing the different visual properties of graphs had been demonstrated in prior reading research—(1) perimetric complexity, sensitive to the ratio of a written form to its surrounding white space (Pelli, Burns, Farell, & Moore-Page, 2006); (2) number of disconnected components, sensitive to discontinuity (Gibson, 1969); (3) number of connected points, sensitive to continuity (Lanthier, Risko, Stolz, & Besner, 2009); and (4) number of simple features, sensitive to the strokes that compose graphs (Wu, Zhou, & Shu, 1999). In our analysis of the complexity of 21,550 graphs, we (a) determined the complexity variation across writing systems along each dimension, (b) examined the relationships among complexity patterns within and across writing systems, and (c) compared the dimensions in their abilities to differentiate the graphs from different writing systems, in order to predict human perceptual judgments (n = 180) of graphs with varying complexity. The results from the computational and experimental comparisons showed that GraphCom provides a measure of graphic complexity that exceeds previous measures in its empirical validation. The measure can be universally applied across writing systems, providing a research tool for studies of reading and writing.


Connected points Disconnected component Gestalt principles Graphic complexity Perimetric complexity Simple features Writing systems 


Author note

This work was supported by the National Science Foundation (Grant #SBE-0836012) through Pittsburgh Science of Learning Center (PSLC) and “Aim for the Top University Project” of the National Taiwan Normal University and the Ministry of Education, Taiwan, R.O.C. The authors thank Adrian Maries and members in the Perfetti Lab at the University of Pittsburgh for their assistance with various tasks, and all observers for their participation. Moreover, the authors acknowledge the insightful comments of David Share and other, anonymous reviewers.


  1. Ager, S. (1998). Omniglot: A guide to writing systems. In Encyclopedia omniglot. Retrieved from
  2. Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59, 390–412. doi: 10.1016/jmla.2007.12.005 CrossRefGoogle Scholar
  3. Bates, D., Maechler, M., & Dai, B. (2010). lme4: Linear mixed-effects models using S4 classes (R package version 0.999375-37) [Computer software manual]. Retrieved from
  4. Berinsky, A. J., Huber, G. A., & Lenz, G. S. (2012). Evaluating online labor markets for experimental research:’s Mechanical Turk. Political Analysis, 20, 351–368. doi: 10.1093/pan/mpr057 CrossRefGoogle Scholar
  5. Biederman, I. (1987). Recognition-by-components: A theory of human image understanding. Psychological Review, 94, 115–147. doi: 10.1037/0033-295X.94.2.115 CrossRefPubMedGoogle Scholar
  6. Bright, W. (Ed.). (1992). International encyclopedia of linguistics. New York: Oxford University Press.Google Scholar
  7. Buhrmester, M., Kwang, T., & Gosling, S. D. (2011). Amazon’s Mechanical Turk: A new source of inexpensive, yet high-quality, data? Perspectives on Psychological Science, 6, 3–5. doi: 10.1177/1745691610393980 CrossRefPubMedGoogle Scholar
  8. Burnham, K. P., & Anderson, D. R. (2003). Model selection and multimodel inference: A practical information-theoretic approach. New York: Springer.Google Scholar
  9. Chandler, J., Mueller, P., & Paolacci, G. (2014). Nonnaïveté among Amazon Mechanical Turk workers: Consequences and solutions for behavioral researchers. Behavior Research Methods, 46, 112–130. doi: 10.3758/s13428-013-0365-7 CrossRefPubMedGoogle Scholar
  10. Chang, L. Y. (2015). Visual orthographic variation and learning to read across writing system (Unpublished doctoral dissertation). University of Pittsburgh, Pennsylvania.
  11. Chang, L. Y., Plaut, D. C., & Perfetti, C. A. (2016). Visual complexity in orthographic learning: Modeling learning across writing system variations. Scientific Studies of Reading, 20, 64–85.CrossRefGoogle Scholar
  12. Changizi, M. A., & Shimojo, S. (2005). Character complexity and redundancy in writing systems over human history. Proceedings of the Royal Society B, 272, 267–275.CrossRefPubMedPubMedCentralGoogle Scholar
  13. Changizi, M. A., Zhang, Q., Ye, H., & Shimojo, S. (2006). The structures of letters and symbols throughout human history are selected to match those found in objects in natural scenes. American Naturalist, 167, E117–E139.CrossRefPubMedGoogle Scholar
  14. Chen, Y. P., Allport, D. A., & Marshall, J. C. (1996). What are the functional orthographic units in Chinese word recognition: The stroke or the Stroke pattern? Quarterly Journal of Experimental Psychology, 49, 1024–1043.CrossRefGoogle Scholar
  15. Chen, H. C., Chang, L. Y., Chiou, Y. S., Sung, Y. T., & Chang, K. E. (2011). Construction of Chinese orthographic database for Chinese character instruction. Bulletin of Educational Psychology, 43, 269–290.Google Scholar
  16. Chikhman, V., Bondarko, V., Danilova, M., Goluzina, A., & Shelepin, Y. (2012). Complexity of images: Experimental and computational estimates compared. Perception, 41, 631–647. doi: 10.1068/p6987 CrossRefPubMedGoogle Scholar
  17. Coen-Cagli, R., & Schwartz, O. (2013). The impact on midlevel vision of statistically optimal divisive normalization in V1. Journal of Vision, 13(8), 1–20. doi: 10.1167/13.8.13 CrossRefGoogle Scholar
  18. Cook, V., & Bassetti, B. (2005). An introduction to researching second language writing systems. In V. Cook & B. Bassetti (Eds.), Second language writing systems (pp. 1–67). Clevedon: Multilingual Matters.Google Scholar
  19. Daniels, P. T. (1990). Fundamentals of grammatology. Journal of the American Oriental Society, 110, 727–731.CrossRefGoogle Scholar
  20. Demetriou, A., Kui, Z. X., Spandoudis, G., Christou, C., Kyriakides, L., & Platsidou, M. (2005). The architecture, dynamics, and development of mental processing: Greek, Chinese, or universal? Intelligence, 33, 109–141.CrossRefGoogle Scholar
  21. Ehrenstein, W. H. (2008). Gestalt psychology. In Encyclopedia of neuroscience (pp. 1721–1724). New York: Springer.Google Scholar
  22. Fiset, D., Blais, C., Ethier-Majcher, C., Arguin, M., Bub, D., & Gosselin, F. (2008). Features for identification of uppercase and lowercase letters. Psychological Science, 19, 1161–1168.CrossRefPubMedGoogle Scholar
  23. Frost, R. (2012). Towards a universal model of reading. Behavioral and Brain Sciences, 35, 263–279. doi: 10.1017/S0140525X11001841 CrossRefPubMedPubMedCentralGoogle Scholar
  24. Gelb, I. J. (1952). A study of writing. Chicago: University of Chicago Press.Google Scholar
  25. Gibson, E. J. (1969). Principles of perceptual learning and development. New York: Meredith.Google Scholar
  26. Grainger, J., Rey, A., & Dufau, S. (2008). Letter perception: From pixels to pandemonium. Trends in Cognitive Sciences, 12, 381–387. doi: 10.1016/j.tics.2008.06.006 CrossRefPubMedGoogle Scholar
  27. Grill-Spector, K., & Malach, R. (2004). The human visual cortex. Annual Review of Neuroscience, 27, 649–677. doi: 10.1146/annurev.neuro.27.070203.144220 CrossRefPubMedGoogle Scholar
  28. Horton, J. J., Rand, D. G., & Zeckhauser, R. J. (2011). The online laboratory: Conducting experiments in a real labor market. Experimental Economics, 14, 3990425.CrossRefGoogle Scholar
  29. Hubel, D. H., & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. Journal of Physiology, 160, 251–260.CrossRefGoogle Scholar
  30. Hubel, D. H., & Wiesel, T. N. (1965). Receptive fields and functional architecture in two non-striate visual areas (18 and 19) of the cat. Journal of Neurophysiology, 28, 229–289.CrossRefPubMedGoogle Scholar
  31. Jiang, Y. V., Shim, W. M., & Makovski, T. (2008). Visual working memory for line orientations and face identities. Perception & Psychophysics, 70, 1581–1591. doi: 10.3758/PP.70.8.1581 CrossRefGoogle Scholar
  32. Katz, L., & Frost, R. (1992). Reading in different orthographies: The orthographic depth hypothesis. In R. Frost & L. Katz (Eds.), Orthography, phonology, morphology, and meaning (pp. 67–84). Amsterdam: North-Holland.CrossRefGoogle Scholar
  33. Koffka, K. (1963). Principles of Gestalt psychology. New York: Harcourt, Brace & World (Original work published 1935).Google Scholar
  34. Lanthier, S. N., Risko, E. F., Stolz, J. A., & Besner, D. (2009). Not all visual features are created equal: Early processing in letter and word recognition. Psychonomic Bulletin & Review, 16, 67–73. doi: 10.3758/PBR.16.1.67 CrossRefGoogle Scholar
  35. Lavine, L. O. (1977). Differentiation of letterlike forms in prereading children. Developmental Psychology, 13, 89–94. doi: 10.1037/0012-1649.13.2.89 CrossRefGoogle Scholar
  36. Lehmann, E. L. (1986). Testing statistical hypotheses (2nd ed.). New York: Springer.CrossRefGoogle Scholar
  37. Levin, I., & Bus, A. G. (2003). How is emergent writing based on drawing? Analyses of children’s products and their sorting by children and mothers. Developmental Psychology, 39, 891–905. doi: 10.1037/0012-1649.39.5.891 CrossRefPubMedGoogle Scholar
  38. Liu, D., Chen, X., & Wang, Y. (2016). The impact of visual–spatial attention on reading and spelling in Chinese children. Reading and Writing, 29, 1435–1447. doi: 10.1007/s11145-016-9644-x CrossRefGoogle Scholar
  39. McBride-Chang, C., Zhou, Y., Cho, J.-R., Aram, D., Levin, I., & Tolchinsky, L. (2011). Visual spatial skill: A consequence of learning to read? Journal of Experimental Child Psychology, 109, 256–262. doi: 10.1016/j.jecp.2010.12.003 CrossRefPubMedGoogle Scholar
  40. Ministry of Education in Japan. (2015). Official list of kyōiku kanji by grade. Retrieved from the Ministry of Education, Culture, Sports, Science and Technology–Japan website,
  41. Mueller, S. T., & Weidemann, C. T. (2012). Alphabetic letter identification: Effects of perceivability, similarity, and bias. Acta Psychologica, 139, 19–37. doi: 10.1016/j.actpsy.2011.09.014 CrossRefPubMedGoogle Scholar
  42. Nag, S. (2007). Early reading in Kannada: The pace of acquisition of orthographic knowledge and phonemic awareness. Journal of Research in Reading, 30, 7–22.CrossRefGoogle Scholar
  43. Nag, S. (2008). Kannada vocabulary test. Bangalore: Promise Foundation.Google Scholar
  44. Nag, S. (2014). Alphabetism and the science of reading: From the perspective of the akshara languages. Frontiers in Psychology, 5, 866. doi: 10.3389/fpsyg.2014.00866 CrossRefPubMedPubMedCentralGoogle Scholar
  45. Nag, S., Caravolas, M., & Snowling, M. J. (2011). Beyond alphabetic processes: Literacy and its acquisition in the alphasyllabic languages. Reading and Writing, 24, 615–622.CrossRefGoogle Scholar
  46. Nag, S., & Snowling, M. J. (2011). Cognitive profiles of poor readers of Kannada. Reading and Writing, 24, 657–676.CrossRefGoogle Scholar
  47. Nag, S., Snowling, M., Quinlan, P., & Hulme, C. (2014). Child and symbol factors in learning to read a visually complex writing systems. Scientific Studies of Reading, 18, 309–324. doi: 10.1080/10888438.2014.892489 CrossRefGoogle Scholar
  48. Nag, S., Treiman, R., & Snowling, M. J. (2010). Learning to spell in an alphasyllabary: The case of Kannada. Writing Systems Research, 2, 41–52.CrossRefGoogle Scholar
  49. Pelli, D. G., Burns, C. W., Farell, B., & Moore-Page, D. C. (2006). Feature detection and letter identification. Vision Research, 46, 4646–4674. doi: 10.1016/j.visres.2006.04.023 CrossRefPubMedGoogle Scholar
  50. Perfetti, C. A. (2003). The universal grammar of reading. Scientific Studies of Reading, 7, 3–24.CrossRefGoogle Scholar
  51. Perfetti, C. A., & Harris, L. N. (2013). Reading universals are modulated by language and writing system. Language Learning and Development, 9, 296–316. doi: 10.1080/15475441.2013.813828 CrossRefGoogle Scholar
  52. Perfetti, C. A., & Verhoeven, L. (in press). Learning to reading across languages and writing systems. Cambridge, UK: Cambridge University Press.Google Scholar
  53. Reas, C., & Fry, B. (2010). Getting started with processing. Sebastopol: O’Reilly.Google Scholar
  54. Rimzhim, A., Katz, L., & Fowler, C. A. (2014). Brahmi-derived orthographies are typologically aksharik but functionally predominantly alphabetic. Writing Systems Research, 6, 41–53. doi: 10.1080/17586801.2013.855618 CrossRefGoogle Scholar
  55. Robins, S., & Treiman, R. (2009). Learning about writing begins informally. In D. Abram & O. Korat (Eds.), Literacy development and enhancement across orthographies and cultures (pp. 17–29). New York: Springer.Google Scholar
  56. Sayim, B., & Cavanagh, P. (2011). What line drawings reveal about the visual brain. Frontiers in Human Neuroscience, 5(118), 1–4. doi: 10.3389/fnhum.2011.00118 Google Scholar
  57. Seidenberg, M. S. (2011). Reading in different writing systems: One architecture, multiple solutions. In P. D. McCardle, B. Miller, J. R. Lee, & O. J. L. Tzeng (Eds.), Dyslexia across languages: Orthography and the brain–gene–behavior link (pp. 146–168). New York: Paul Brookes.Google Scholar
  58. Seymour, P. H. K., Aro, M., & Erskine, J. M. (2003). Foundation literacy acquisition in European orthographies. British Journal of Psychology, 94, 143–174.CrossRefPubMedGoogle Scholar
  59. Share, D. L., & Daniels, P. T. (2016). Aksharas, alphasyllabaries, abugidas, alphabets and orthographic depth: Reflections on Rimzhim, Katz and Folwer (2014). Writing System Research, 8, 17–31. doi: 10.1080/17586801.2015.1016395 CrossRefGoogle Scholar
  60. Shen, H. H., & Ke, C. (2007). Radical awareness and word acquisition among nonnative learners of Chinese. Modern Language Journal, 91, 97–111.CrossRefGoogle Scholar
  61. Simcox, T., & Fiez, J. (2014). Collecting response times using Amazon Mechanical Turk and Adobe Flash. Behavior Research Methods, 46, 95–111. doi: 10.3758/s13428-013-0345-y CrossRefPubMedPubMedCentralGoogle Scholar
  62. Simpson, I. C., Mousikou, P., Montoya, J. M., & Defior, S. (2013). A letter visual-similarity matrix for Latin-based alphabets. Behavior Research Methods, 45, 431–439.CrossRefPubMedGoogle Scholar
  63. Spillmann, L., & Ehrenstein, W. H. (2004). Gestalt factors in the visual neurosciences. In L. Chalupa & J. S. Werner (Eds.), The visual neurosciences (pp. 1573–1589). Cambridge: MIT Press.Google Scholar
  64. Sprouse, J. (2011). A validation of Amazon Mechanical Turk for the collection of acceptability judgments in linguistic theory. Behavior Research Methods, 43, 155–167. doi: 10.3758/s13428-010-0039-7 CrossRefPubMedGoogle Scholar
  65. Stephens, M. A. (1974). EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730–737.CrossRefGoogle Scholar
  66. Su, Y.-F., & Samuels, S. J. (2010). Developmental changes in character-complexity and word-length effects when reading Chinese script. Reading and Writing, 23, 1085–1108. doi: 10.1007/s11145-009-9197-3 CrossRefGoogle Scholar
  67. Szwed, M., Cohen, L., Qiao, E., & Dehaene, S. (2009). The role of invariant line junctions in object and visual word recognition. Vision Research, 49, 718–725. doi: 10.1016/j.visres.2009.01.003 CrossRefPubMedGoogle Scholar
  68. Tamaoka, K., & Kiyama, S. (2013). The effects of visual complexity for Japanese kanji processing with high and low frequencies. Reading and Writing, 26, 205–223. doi: 10.1007/s11145-012-9363-x CrossRefGoogle Scholar
  69. Tokowicz, N., Michael, E., & Kroll, J. F. (2004). The roles of study abroad experience and working memory capacity in the types of errors made during translation. Bilingualism: Language and Cognition, 7, 255–272.CrossRefGoogle Scholar
  70. Treiman, R., Hompluem, L., Gordon, J., Decker, K., & Markson, L. (2016). Young children’s knowledge of the symbolic nature of writing. Child Development, 87, 583–592. doi: 10.1111/cdev.12478 CrossRefPubMedPubMedCentralGoogle Scholar
  71. Treiman, R., & Kessler, B. (2011). Similarities among the shapes of writing and their effects on learning. Written Language and Literacy, 14, 39–57.CrossRefPubMedPubMedCentralGoogle Scholar
  72. Treiman, R., & Kessler, B. (2014). How children learn to write words. New York: Oxford University Press.CrossRefGoogle Scholar
  73. Treiman, R., Mulqueeny, K., & Kessler, B. (2014). Young children’s knowledge about the spatial layout of writing. Writing System Research, 7, 235–244. doi: 10.1080/17586801.2014.924386 CrossRefGoogle Scholar
  74. Troncoso, X. G., Macknik, S. L., & Martinez-Conde, S. (2011). Visual prosthetics (G. Dagnelie, Ed.). Boston, MA: Springer. doi: 10.1007/978-1-4419-0754-7
  75. Van Essen, D. C., Anderson, C. H., & Felleman, D. J. (1992). Information processing in the primate visual system: An integrated systems perspective. Science, 255, 419–423. doi: 10.1126/science.1734518 CrossRefPubMedGoogle Scholar
  76. Wang, Y., McBride-Chang, C., & Chan, S. (2014). Correlates of Chinese kindergarteners’ word reading and writing: The unique role of copying skills? Reading and Writing, 27, 1281–1302. doi: 10.1111/1467-9817.12016 CrossRefGoogle Scholar
  77. Wasserman, L. (2006). All of statistics: A concise course in statistical inference (pp. 218–222). New York: Springer.Google Scholar
  78. Watson, A. B. (2012). Perimetric complexity of binary digital images: Notes on calculation and relation to visual complexity. Mathematica Journal, 14, 1–41. doi: 10.3888/tmj.14-5 CrossRefGoogle Scholar
  79. Watt, W. C. (1983). Grade der Systemhaftigkeit: Zur Homogenitat der Alphabetschrift [Degrees of systematicity: On the homogeneity of the alphabetic script]. Zeitschrift fur Semiotik, 5, 371–399.Google Scholar
  80. Watt, W. C. (1994). Curves as angles. In Writing systems and cognition—Perspectives from psychology, physiology, linguistics, and semiotics (pp. 215–246). Amsterdam, The Netherlands: Springer.Google Scholar
  81. Winskel, H. (2010). Spelling development in Thai children. Journal of Cognitive Science, 11, 7–35.CrossRefGoogle Scholar
  82. Wu, N., Zhou, X., & Shu, H. (1999). Sublexical processing in reading Chinese: A development study. Language and Cognitive Processes, 14, 503–524.CrossRefGoogle Scholar
  83. Wydell, T. N. (2012). Cross-cultural/linguistic differences in the prevalence of developmental dyslexia and the hypothesis of granularity and transparency. In T. N. Wydell & L. Fern-Pollak (Eds.), Dyslexia: A comprehensive and international approach (pp. 1–14). Rijeka: InTech.CrossRefGoogle Scholar
  84. Yin, L., & McBride, C. (2015). Chinese kindergarteners learn to read characters analytically. Psychological Science, 26, 424–432.CrossRefPubMedGoogle Scholar
  85. Ziegler, J. C., & Goswami, U. (2005). Reading acquisition, developmental dyslexia, and skilled reading across languages: A psycholinguistic grain size theory. Psychological Bulletin, 131, 3–29. doi: 10.1037/0033-2909.131.1.3 CrossRefPubMedGoogle Scholar

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© Psychonomic Society, Inc. 2017

Authors and Affiliations

  1. 1.Department of Applied Chinese Language and CultureNational Taiwan Normal UniversityTaipeiTaiwan
  2. 2.Department of StatisticsUniversity of WashingtonSeattleUSA
  3. 3.Learning Research and Development CenterUniversity of PittsburghPittsburghUSA

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