Skip to main content
SpringerLink
Log in

Network Theory

  • Chapter
  • First Online:
Book cover Dual Phase Evolution

  • 716 Accesses

Abstract

Networks are structures composed of sets of nodes and edges.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

References

  1. A.L. Barabási, R. Albert, Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  2. A.L. Barabási, R. Albert, H. Jeong, Mean-field theory for scale-free random networks. Phys. A 272, 173–187 (1999)

    Google Scholar 

  3. D.J. Watts, S.H. Strogatz, Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  4. S. Wasserman, K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, 1994)

    Book  Google Scholar 

  5. M.E.J. Newman, S.H. Strogatz, D.J. Watts, Random graphs with arbitrary degree distributions and their applications. Phys.Rev. E 64, 026118 (2001)

    Article  Google Scholar 

  6. Ed M. Kochen, The Small World (Ablex, Norwood, NJ, 1989)

    Google Scholar 

  7. M.D. Humphries, K. Gurney, Network ’small-world-ness’: a quantitative method for determining canonical network equivalence. PLOS ONE 3(4), 1–10 (2008)

    Article  Google Scholar 

  8. M.E.J. Newman, Mixing patterns in networks. Phys. Rev. E 67, 026126 (2003)

    Article  MathSciNet  Google Scholar 

  9. R. Pastor-Satorras, A. Vázquez, A. Vespignani, Dynamical and correlation properties of the internet. Phys. Rev. Lett. 87(25), 258701 (2001)

    Article  Google Scholar 

  10. M.E.J. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89(20), 208701 (2002)

    Article  Google Scholar 

  11. F. Jacob, J. Monod, Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3, 318–356 (1961)

    Article  Google Scholar 

  12. G. Halder, P. Callerts, W.J. Gehring, Induction of ectopic eyes by targeted expression of the eyeless gene in drosophila. Science 267, 1788–1792 (1995)

    Article  Google Scholar 

  13. T.F. Hansen, Is modularity necessary for evolvability? Remarks on the relationship between pleiotropy and evolution. Biosystems 69, 83–94 (2003)

    Article  Google Scholar 

  14. A. Wagner, Does evolutionary plasticity evolve? Evolution 50(3), 1008–1023 (1996)

    Article  Google Scholar 

  15. G.P. Wagner, L. Altenberg, Complex adaptations and the evolution of evolvability. Evolution 50, 967–976 (1996)

    Article  Google Scholar 

  16. S.L. Pimm, Food Webs (Chapman and Hall, London, 1982)

    Book  Google Scholar 

  17. M.E.J. Newman, M. Girvan, Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)

    Article  Google Scholar 

  18. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, U. Alon, Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)

    Article  Google Scholar 

  19. U. Alon, Network motifs: theory and experimental approaches. Natl. Rev. Genet. 8(6), 450–461 (2007)

    Article  Google Scholar 

  20. D.G. Green, S. Sadedin, Interactions matter—complexity in landscapes and ecosystems. Ecol. Complex. 2(2), 117–130 (2005)

    Article  Google Scholar 

  21. R. Levins, The search for the macroscopic in ecosystems, in New Directions in the Analysis of Ecological Systems II, ed. by G.S. Innes (Simulation Councils, La Jolla, 1977), pp. 213–222

    Google Scholar 

  22. I.R. Noble, R.O. Slatyer, The use of vital attributes to predict successional changes in plant communities subject to recurrent disturbance. Vegetatio 43, 5–21 (1980)

    Article  Google Scholar 

  23. R.H. Bradbury, Y. Loya, A heuristic analysis of spatial patterns of hermatypic corals at eilat red sea. Am. Nat. 112, 493–507 (1978)

    Article  Google Scholar 

  24. P. Hogeweg, B. Hesper, Two predators and one prey in a patchy environment: an application of micmac modeling. J. Theor. Biol. 93, 411–432 (1981)

    Article  MathSciNet  Google Scholar 

  25. A. Bairoch, Prosite: a dictionary of sites and patterns in protein. Nucleic Acids Res. 19, 2241–2245 (1991)

    Article  Google Scholar 

  26. P. Ribeiro, F. Silva, M. Kaiser, Strategies for network motifs discovery, e-science, in Fifth IEEE International Conference on e-Science (2009), pp. 80–87

    Google Scholar 

  27. A. Wuensche, M.J. Lesser, The global dynamics of cellular automata. An atlas of basin of attraction fields of one-dimensional cellular automata (Addison-Wesley, Reading MA, 1992)

    Google Scholar 

  28. S. Wolfram, Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986)

    MATH  Google Scholar 

  29. C.G. Langton, Computation at the edge of chaos: phase transitions and emergent computation. Physica D 42(1–3), 12–37 (1990)

    Article  MathSciNet  Google Scholar 

  30. E. Albert, A.L. Barabási, Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)

    Article  MATH  Google Scholar 

  31. M.E.J. Newman, The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  32. B.A. Huberman, The Laws of the Web (MIT Press, Cambridge, 2001)

    Google Scholar 

  33. J. Scott, Social Network Analysis: A Handbook (Sage Publications, London, 2000)

    Google Scholar 

  34. H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A.L. Barabási, The large-scale organization of metabolic networks. Nature 407(6804), 651–654 (2000)

    Article  Google Scholar 

  35. S.L. Pimm, Food Webs (University of Chicago, Chicago, 2002)

    Google Scholar 

  36. M. Prokopenko, P. Wang, D.C. Price, P. Valencia, M. Foreman, A.J. Farmer, Self-organizing hierarchies in sensor and communication networks. Artificial Life 11(4), 407–426 (2005)

    Article  Google Scholar 

  37. A. Ghoneim, H.A. Abbass, M. Barlow, Characterizing game dynamics in two-player strategy games using network motifs. IEEE Trans. Sys. Man Cyber. B 38(3), 682–690 (2008)

    Article  Google Scholar 

  38. M. Prokopenko, F. Boschetti, A. Ryan, An information-theoretic primer on complexity, self-organisation and emergence. Complexity 15(1), 11–28 (2009)

    Article  MathSciNet  Google Scholar 

  39. C. Gershenson, Towards self-organizing bureaucracies. Int. J. Public Inf. Syst. 1, 1–24 (2008)

    Google Scholar 

  40. M. Girvan, M.E.J. Newman, Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99, 7821 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  41. J. Liu, W. Zhong, H.A. Abbass, D. Green, Separated and overlapping community detection in complex networks using multiobjective evolutionary algorithms, in Proceedings of IEEE 2010 Congress on Evolutionary Computation (CEC) (2010)

    Google Scholar 

  42. J. Leskovec, D. Chakrabarti, J. Kleinberg, C. Faloutsos, Z. Ghahramani, Kronecker graphs: an approach to modeling networks. J. Mach. Learn. Res. 11, 985–1042 (2010)

    MathSciNet  MATH  Google Scholar 

  43. P. Erdős, A. Rényi, On the evolution of random graphs. Mat. Kutato. Int. Koz 1(5), 17–61 (1960)

    Google Scholar 

  44. R. Kumar, P. Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins, E. Upfal, Stochastic models for the web graph, in Proceedings of the 41st Annual Symposium on Foundations of Computer Science (2000)

    Google Scholar 

  45. D.M. Pennock, G.W. Flake, S. Lawrence, E.J. Glover, C.L. Giles, Winners don’t’ take all: characterizing the competition for links on the web. Proc. Natl. Acad. Sci. 99(8), 5207–5211 (2002)

    Google Scholar 

  46. J. Leskovec, J. Kleinberg, C. Faloutsos, Graphs over time: densification laws, shrinking diameters and possible explanations, in KDD (2005)

    Google Scholar 

  47. A. Blum, H. Chan, M. Rwebangira, A random-surfer web-graph model, in ANALCO’06: Proceedings of the 3rd Workshop on Analytic Algorithmics and Combinatorics (2006)

    Google Scholar 

  48. M.C. González, P.G. Lind, H.J. Herrmann, System of mobile agents to model social networks. Phys. Rev. Lett. 96, 088702 (2006)

    Article  Google Scholar 

  49. J.M. Kumpula, J.P. Onnela, J. Saramki, K. Kaski, J. Kertész, Emergence of communities in weighted networks. Phys. Rev. Lett. 99, 228701 (2007)

    Article  Google Scholar 

  50. A. Rapoport, W.J. Horvath, A study of a large sociogram. Behav. Sci 6, 279–291 (1961)

    Article  Google Scholar 

  51. B. Hu, X.-Y. Jiang, J.-F. Ding, Y.-B. Xie, B.-H. Wang, A weighted network model for interpersonal relationship evolution. Physica A 353, 576–594 (2005)

    Article  Google Scholar 

  52. N. Guelzim, S. Bottani, P. Bourgine, F. Képes, Topological and causal structure of the yeast transcriptional regulatory network. Nat. Genet. 31, 60–63 (2002)

    Article  Google Scholar 

  53. S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, UK, 2003)

    Book  Google Scholar 

  54. J. Ohkubo, T. Horiguchi, Complex neworks by non-growing model with preferential rewiring process. J. Phys. Soc. Jpn 74(4), 1334–1340 (2005)

    Article  Google Scholar 

  55. G. Bianconi, A.L. Barabási, Competition and multiscaling in evolving networks. Europhys. Lett. 54, 436–442 (2001)

    Article  Google Scholar 

  56. T.S. Evans, A.D.K. Plato, Exact solution for the time evolution of network rewiring models. Phys. Rev. E 75, 056101 (2007)

    Article  MathSciNet  Google Scholar 

  57. T.S. Evans, Exact solutions for network rewiring models. Eur. Phys. J. B. 56, 65–69 (2007)

    Article  Google Scholar 

  58. Y.B. Xie, T. Zhou, B.H. Wang, Scale-free networks without growth. Phys. A 387, 1683–1688 (2008)

    Article  Google Scholar 

  59. J. Lindquist, J. Ma, P. Driessche, F.H. Willeboordse, Network evolution by different rewiring schemes. Physica D 238, 370–378 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  60. S. Johnson, J.J. Torres, Marro, Nonlinear preferential rewiring in fixed-size networks as a diffusion process. Phys. Rev. E 79, 050104(R) (2009)

    Google Scholar 

  61. X.-J. Xu, X.-M. Hu, L.-J. Zhang, Network evolution by nonlinear preferential rewiring of edges. Physica A 390, 2429–2434 (2011)

    Article  MathSciNet  Google Scholar 

  62. W. Zhong, J. Liu, Comment on “scale-free networks without growth". Physica A 391, 263–265 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Information Technology, Monash, Clayton, Australia

    David G. Green

  2. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi’an, People’s Republic of China

    Jing Liu

  3. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT, Australia

    Hussein A. Abbass

Authors
  1. David G. Green
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hussein A. Abbass
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David G. Green .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Green, D.G., Liu, J., Abbass, H.A. (2014). Network Theory. In: Dual Phase Evolution. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8423-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-8423-4_2

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-8422-7

  • Online ISBN: 978-1-4419-8423-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation