Complex Networks Theory

  • Andreas Kemper
Part of the Contributions to Management Science book series (MANAGEMENT SC.)


This chapter provides a summary of relevant insights into complex networks theory. It is the foundation for the development of network theoretical hypotheses and the respective network methodology. In the first step, a brief overview on the background of complex networks research is provided, before relevant structural and locations properties of networks are presented. The network measures are used to illustrate insights into the structure and on the dynamics of networks. At the end of this chapter, research hypotheses are developed concerning the open research questions on network network-centric valuation in software markets. They are challenged with the complex networks diffusion simulator that is developed in the following chapter.


Complex Network Degree Distribution Cluster Coefficient Degree Correlation Giant Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Adamic, L., & Huberman, B. (2000). Power-law distribution of the world wide web. Science,287, 2115.CrossRefGoogle Scholar
  2. Albert, R. (2001). Statistical Mechanics of Complex Networks. Ph. D. book, University of Notre Dame.Google Scholar
  3. Albert, R., & Barabasi, A. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics,74, 47–97.CrossRefGoogle Scholar
  4. Albert, R., Jeong, H., & Barabasi, A. (1999). Diameter of the world-wide web. Nature,401, 130–131.CrossRefGoogle Scholar
  5. Amaral, L., Scala, A., Barthlmy, M., & Stanley, H. (2000). Classes of small-world networks. Proceedings of the National Academy of Sciences of the United States of America,97, 11149–11152.CrossRefGoogle Scholar
  6. Anderson, R., & May, R. (1991). Infectious diseases of humans. variety of mathematical models for epidemics: Oxford University Press.Google Scholar
  7. Bailey, N. (1975). The mathematical theory of infectious diseases and its applications. New York: Hafner Press.Google Scholar
  8. Banks, D., & Carley, K. (1996). Models for network evolution. Journal of Mathematical Sociology,21, 173–196.CrossRefGoogle Scholar
  9. Bar-Yam, Y. (1997). Dynamics of complex systems. Reading MA: Perseus.Google Scholar
  10. Barabasi, A. (2002). Linked - The new science of networks. Cambridge: Perseus. Network Theory.Google Scholar
  11. Barabasi, A., & Albert, R. (1999). Emergence of scaling in random networks. Science,286, 509–512.CrossRefGoogle Scholar
  12. Barabasi, A., Albert, R., & Jeong, H. (1999). Mean-field theory for scale-free random networks. Physica A: Statistical Mechanics and its Applications,272, 173–187.CrossRefGoogle Scholar
  13. Barabasi, A., Albert, R., Jeong, H., & Bianconi, G. (2000). Power-law distribution of the world wide web. Science,287, 2115a.CrossRefGoogle Scholar
  14. Batten, D., Cast, J., & Thord, R. (1995). Networks in action - communication, economics and human knowledge. Berlin: Springer. Networks Theory, Networks as Dynamic Systems, Infrastructure Networks, Economic Networks.Google Scholar
  15. Bianconi, G., & Barabasi, A. (2001a). BoseEinstein condensation in complex networks. Physical Review Letters,86, 5632–5635.CrossRefGoogle Scholar
  16. Bollobas, B. (1985). Random Graphs. London: Academic.Google Scholar
  17. Bollobas, B. (2001). Random Graphs (2nd ed.). New York: Academic.Google Scholar
  18. Bollobas, B., & Riordan, O. (2006). Percolation. Cambrige/MA: Cambridge University Press.Google Scholar
  19. Broadbent, S., & Hammersley, J. (1957). Percolation processes: I. crystals and mazes. Proceedings of the Cambridge Philosophical Society,53, 629–641.Google Scholar
  20. Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Ra-jagopalan, S., Stata, R., Tomkins, A., & Wiener, J. (2000). Graph structure in the web. Computer Networks,33, 309–320.CrossRefGoogle Scholar
  21. Buchanan, M. (2002). Nexus: Small worlds and the groundbreaking science of networks. New York: W.W. Norton & Company Inc.Google Scholar
  22. Callaway, D., Hopcroft, J., Kleinberg, J. Newman, M., & Strogatz, S. (2001). Are randomly grown graphs really random? Physical Review E,64, 041902.Google Scholar
  23. Cauchy, A. (1813). Recherche sur les polydres - premier mmoire. Journal de l’Ecole Polytechnique 9,Cahier 16, 66–86.Google Scholar
  24. Cayley, A. (1875). ber die Analytischen Figuren, welche in der Mathematik Bume genannt werden und ihre Anwendung auf die Theorie chemischer Verbindungen. Berichte der deutschen Chemischen Gesellschaft,8, 1056–1059.CrossRefGoogle Scholar
  25. Cohen, R., Erez, K., ben Avraham, D., & Havlin, S. (2000). Resilience of the internet to random breakdowns. Physical Review Letters,85, 4626–4628.Google Scholar
  26. Cohen, R., Erez, K., ben Avraham, D., & Havlin, S. (2001). Breakdown of the internet under intentional attack. Physical Review Letters,86, 3682–3685.Google Scholar
  27. Dorogovtsev, S., & Mendes, J. (2001). Effect of the accelerating growth of communications networks on their structure. Physical Review E,63, 025101.CrossRefGoogle Scholar
  28. Dorogovtsev, S., & Mendes, J. (2002). Evolution of networks. Advances in Physics,51, 1079–1187.CrossRefGoogle Scholar
  29. Dorogovtsev, S., Mendes, J., & Samukhin, A. (2001). Giant strongly connected component of directed networks. Physical Review E,64, 025101.CrossRefGoogle Scholar
  30. Duden. (1989). Duden Etymologie: Herkunftswörterbuch der deutschen Sprache (2nd ed.). Mannheim: Duden.Google Scholar
  31. Ebel, H., Mielsch, L., & Bornholdt, S. S. (2002). Scale-free topology of e-mail networks. Physical Review E,66, 035103.CrossRefGoogle Scholar
  32. Erdos, P., & Renyi, A. (1959). On random graphs. Publicationes Mathematicae,6, 290–297.Google Scholar
  33. Everitt, B. (1974). Cluster analysis. New York: John Wiley.Google Scholar
  34. Faloutsos, M., Faloutsos, P., & Faloutsos, C. (1999). On power-law relationships of the internet topology. Computer Communications Review,29, 251–262.CrossRefGoogle Scholar
  35. Fell, D., & Wagner, A. (2000). The small world of metabolism. Nature Biotechnology,18, 1121–1122.CrossRefGoogle Scholar
  36. Freeman, L. (1977). A set of measures of centrality based upon betweenness. Sociometry,40, 35–41.CrossRefGoogle Scholar
  37. Fronczak, A., Holyst, J., Jedynak, M., & Sienkiewicz, J. (2002). Higher order clustering coefficients in barabasi-albert networks. Physica A: Statistical Mechanics and its Applications,316, 688–694.CrossRefGoogle Scholar
  38. Garfield, E. (1979). It’s a small world after all. Current Contents,43, 5–10.Google Scholar
  39. Grassberger, P. (1983). On the critical behavior of the general epidemic process and dynamical percolation. Mathematical Biosciences,63, 157–172.CrossRefGoogle Scholar
  40. Guare, J. (1990). Six degrees of separation: A play. New York: Vintage.Google Scholar
  41. Harary, F., Morman, R., & Cartwright, D. (1965). Structural Models: An Introduction to the Theory of Directed Graphs. New York: John Wiley & Sons.Google Scholar
  42. Hayes, B. (2000a). Graph theory in practice: Part i. American Scientist,88, 9–13.Google Scholar
  43. Hethcote, H. (2000). Mathematics of infectious diseases. SIAM Review,42, 599–653.CrossRefGoogle Scholar
  44. Huillier, S. (1861). Mmoire sur la polydromtrie. Annales de Mathmatiques,3, 169189.Google Scholar
  45. Janson, S., Luczak, T., & Rucinski, A. (1999). Random Graphs. New York: John Wiley.Google Scholar
  46. Jeong, H., Mason, S., Barabasi, A., & Oltvai, Y. (2001). Lethality and centrality in protein networks. Nature,411, 41–42.CrossRefGoogle Scholar
  47. Jeong, H., Tombor, B., Albert, R., Oltvai, Z., & Barabasi, A. (2000). The large-scale organization of metabolic networks. Nature,407, 651–654.CrossRefGoogle Scholar
  48. Karonski, M. (1982). A review of random graphs. Journal of Graph Theory,6, 349–389.CrossRefGoogle Scholar
  49. Kemper, A. (2006). Modelling network growth with network theory and cellular automata. Journal of Modelling in Management,1, 75–84.CrossRefGoogle Scholar
  50. Kirchhoff, G. (1847). ber die Auflsung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Strme gefhrt wird. Annals of Physical Chemistry,72, 497–508.CrossRefGoogle Scholar
  51. Klovdahl, A., Potterat, J., Woodhouse, D., Muth, J., Muth, S., & Darrow, W. (1994). Social networks and infectious disease: The colorado springs study. Social Science & Medicine,38, 79–88.CrossRefGoogle Scholar
  52. Krapivsky, P., Rodgers, G., & Redner, S. (2001). Degree distributions of growing networks. Physical Review Letters,86, 5401–5404.CrossRefGoogle Scholar
  53. Liljeros, F., Edling, C., Amaral, L., Stanley, H., & Aberg, Y. (2001). The web of human sexual contacts. Nature,411, 907–908.CrossRefGoogle Scholar
  54. Luterotti, E., & Stefanelli, U. (2002). Existence result for the one-dimensional full model of phase transitions. Journal for Analysis and its Applications,21, 335–350.Google Scholar
  55. Maslov, S., & Sneppen, K. (2002). Specificity and stability in topology of protein networks. Science,296, 910–913.CrossRefGoogle Scholar
  56. McKendrick, A. (1926). Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society,44, 98–130.CrossRefGoogle Scholar
  57. Merton, R. (1968). The matthew effect in science. Science,159, 56–63.CrossRefGoogle Scholar
  58. Milgram, S. (1967). The small world problem. Psychology Today,2, 60–67.Google Scholar
  59. Montoya, J., & Sole, R. (2002). Small world patterns in food webs. Journal of Theoretical Biology,214, 405–412.CrossRefGoogle Scholar
  60. Moreno, J. (1934). Who Shall Survive? Beacon: Beacon House.Google Scholar
  61. Newman, M. (2000). Models of the small world. Journal of statistical physics,101, 819–841.CrossRefGoogle Scholar
  62. Newman, M. (2001a). Clustering and preferential attachment in growing networks. Physical Review E,64, 025102.CrossRefGoogle Scholar
  63. Newman, M. (2002). Assortative mixing in networks. Physical Review Letters,89, 208701.CrossRefGoogle Scholar
  64. Newman, M. (2003a). Mixing patterns in networks. Physical Review E,67(2), 026126.CrossRefGoogle Scholar
  65. Newman, M. (2003b). The structure and function of complex networks. SIAM Review,45, 167–256.CrossRefGoogle Scholar
  66. Newman, M., Barabsi, A., & Watts, D. (2006). The structure and dynamics of networks. NJ: Princeton University Press.Google Scholar
  67. Newman, M., Forrest, S., & Balthrop, J. (2002). Email networks and the spread of computer viruses. Physical Review E,66, 035101.CrossRefGoogle Scholar
  68. Newman, M., & Watts, D. (1999). Scaling and percolation in the small-world network model. Physical Review E,60, 7332–7342.CrossRefGoogle Scholar
  69. Pastor-Satorras, R., Vazquez, A., & Vespignani, A. (2001). Dynamical and correlation properties of the internet. Physical Review Letters,87, 258701.CrossRefGoogle Scholar
  70. Pastor-Satorras, R., & Vespignani, A. (2001a). Epidemic dynamics and endemic states in complex networks. Physical Review E,63, 066117.CrossRefGoogle Scholar
  71. Pennock, D., Flake, G., Lawrence, S., Glover, E., & Giles, C. (2002). Winners don’t take all: Characterizing the competition for links on the web. Proceedings of the National Academy of Sciences of the United States of America,99, 52075211.CrossRefGoogle Scholar
  72. Price, D. (1965). Networks of scientific papers. Science,149, 510–515.CrossRefGoogle Scholar
  73. Price, D. (1976). A general theory of bibliometric and other cumulative advantage processes. Journal of the American Society for Information Science,27, 292–306.CrossRefGoogle Scholar
  74. Rapoport, A. (1957). Contribution to the theory of random and biased nets. Bulletin of Mathematical Biophysics,19, 257–277.CrossRefGoogle Scholar
  75. Sander, L., Warren, C., Sokolov, I., Simon, C., & Koopman, J. (2002). Percolation on disordered networks as a model for epidemics. Mathematical Biosciences,180, 293–305.CrossRefGoogle Scholar
  76. Sattenspiel, L., & Simon, C. (1988). The spread and persistence of infectious diseases in structured populations. Mathematical Biosciences90, 367–383.Google Scholar
  77. Schwartz, N., Cohen, R., ben Avraham, D., Barabási, A., & Havlin, S. (2002). Percolation in directed scale-free networks. Physical Review E,66, 015104.Google Scholar
  78. Scott, J. (2000). Social Network Analysis: A Handbook (2nd ed.). London: Sage Publications.Google Scholar
  79. Simon, H. (1955). On a class of skew distribution functions. Biometrika,42, 425–440.Google Scholar
  80. Simon, H. (1962). The architecture of complexity. Cambridge: MIT. Fundamental Article.Google Scholar
  81. Solomonoff, R., & Rapoport, A. (1951). Connectivity of random nets. Bulletin of Mathematical Biophysics,13, 107–117.CrossRefGoogle Scholar
  82. Strogatz, S. (1994). Nonlinear Dynamics and Chaos. Cambridge: Perseus.Google Scholar
  83. Strogatz, S. (2001). Exploring complex networks. Nature,410, 268–276. Nonlinear Dynamics; Regular Networks of coupled dynamical systems: identical oscilators, non-identical oscilators; Complex Networks architecture: Random, Small-World, Scale-Free networks, Random Graphs; Outlook.Google Scholar
  84. Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry,32, 425–443.CrossRefGoogle Scholar
  85. Verdult, V., & Verhaegen, M. (2000). Bilinear state space systems for nonlinear dynamical modelling. Theory Biosciences,119, 1–9.Google Scholar
  86. von Westarp, F. (2003). Modeling Software Markets - Empirical Analysis, Network Simulations, and Marketing Implications. Heidelberg: Springer.Google Scholar
  87. Wasserman, S., & Faust, K. (1994). Social network theory. Cambridge: Cambridge University Press.Google Scholar
  88. Watts, D. (1999). Small worlds: the dynamics of networks between order and randomness. Princeton: Princeton University Press.Google Scholar
  89. Watts, D., & Strogatz, S. (1998). Collective dynamics of ’small-world’ networks. Nature,393, 440–442.CrossRefGoogle Scholar
  90. Weitzel, T., Wendt, O., & Westarp, F. (2000). Reconsidering network effect theory. European Conference on Information Systems 2000.Google Scholar
  91. Williams, R., & Martinez, N. (2000). Simple rules yield complex food webs. Nature,404, 180–183.CrossRefGoogle Scholar
  92. Yule, G. (1925). A mathematical theory of evolution, based on the conclusions of dr. j. c. willis, f.r.s. Philosophical Transactions of the Royal Society of London, Series B,213, 21–87.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.FrankfurtGermany

Personalised recommendations