SpringerLink
Log in

Graph Theory, Social Network Analysis, and Network Science

  • Chapter
  • First Online:
Network Analysis Literacy

Part of the book series: Lecture Notes in Social Networks ((LNSN))

Abstract

Network analysis provides a versatile framework for modeling complex systems and because of its universal applicability it has been invented and rediscovered in many different disciplines. Each of these disciplines enriches the field by providing its own perspective and its own approaches; the three most prominent disciplines in the area are sociology , graph theory , and statistical physics . As these disciplines follow very different aims, it is vital to understand the different approaches and perspectives. This chapter elaborates and opposes the different approaches to highlight those points which are important for the topic of interest—network analysis literacy.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 117.69
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 149.79
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 149.79
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The book can be found online http://www.asgpp.org/docs/WSS/WSS.html.

  2. 2.

    The history of social network analysis is described in detail in Freeman’s book with the title “The Development of Social Network Analysis—A Study in the Sociology of Science” [23].

  3. 3.

    And numerous others....

  4. 4.

    Vicsek writes : “If a concept is not well defined, it can be abused. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated a range of intellectual fields from physics to linguistics, but with no underlying, unified theory” [58]. While there is no well-defined research area or a clearly stated theory underlying the research, Vicsek states that all complex systems show interacting entities on many levels which leads to a new and unexpected behavior on the next higher level.

  5. 5.

    The term entity is used very often in this book and denotes any kind of subject or object that is clearly discernible from its environment.

  6. 6.

    http://www.youtube.com/watch?v=sROKYelaWbo.

  7. 7.

    The history of the paper is described in the TV documentary “How Kevin Bacon cured cancer” by the Australian Broadcasting Company from 2008. Watts also describes parts of it in his Ph.D. thesis and his second book [60, 61].

  8. 8.

    A protein is a medium sized molecule with complex 3D structure that fulfills various biological functions in a cell. Often, different proteins have to cooperate, e.g., by building protein complexes or by transferring small molecules from one to the other. This cooperation is called protein-protein interaction.

  9. 9.

    Note, however, that Moreno already likened the human society to physical matter in his influential book “Who shall survive”: “Human society has an atomic structure which is analogous to the atomic structure of matter” [43, 3rd edition, p. 69].

  10. 10.

    A similar perspective on the ‘new’ old social physics approach was written by Scott [51].

  11. 11.

    Given a data set and a function which seems to describe the data well, a “fit” tries to find those parameter values which minimize the difference between the function and the data.

  12. 12.

    Social network analysts will rightfully complain that there actually were more complex models than the simple random graph model as described, e.g., by Wasserman and Faust [59].

  13. 13.

    The author of this book confesses to be guilty of this, as well.

  14. 14.

    In this approximation one does not take into account that young persons in general might have a different probability to acquire an infection than the general population.

  15. 15.

    Terrorized by the formula? Bear with me, and give your best to conquer it. The notation P[A|B] means: the probability that A happens if we already know that B has happened.

  16. 16.

    As long as a patient has no symptoms, the same calculation applies to all preventive check-ups made to detect rare diseases like breast cancer or prostate cancer. It is severed by less sensitive and specific tests to detect these illnesses. As a first, positive test usually induces more intrusive and possibly harmful test procedures like a biopsy.

  17. 17.

    So did I.

  18. 18.

    The logical argument for biological networks is slightly different: whenever a mutation forms a more functional network which increases the likelihood of the organism to create offspring, the network is likely to multiply in future generations.

  19. 19.

    Note that actually metabolic reaction networks do support a biological process, namely the transport of energy and information. With a careful modeling, a metabolic reaction network can be an “interactive network”. Similarly, Google uses the link structure of the world wide web to mimic the behavior of a “random surfer” which is a model of the social process of how a person might use the links. Again, the network can also be seen as an interactive network.

References

  1. Ahnert R (2013) Protestant letter networks in the reign of Mary I. In: Book of abstracts of the 4th Leonardo satellite symposium on arts, humanities, and complex networks

    Google Scholar 

  2. Bakan D (1966) The test of statistical significance in psychological research. Psychol Bull 66(6):423–437

    Article  Google Scholar 

  3. Barabási A-L (2002) Linked—the new science of networks. Perseus, Cambridge

    Google Scholar 

  4. Barabási A-L (2005) Taming complexity. Nat Phys 1:68–70

    Article  Google Scholar 

  5. Barabási A-L (to be published) Network science. Cambridge University Press, Cambridge

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Blau PM (1974) Presidential address: parameters of social structure. Amer Sociol Rev 39(5):615–635

    Article  MathSciNet  Google Scholar 

  8. Bollobás B (2001) Random graphs. Cambridge studies in advanced mathematics, vol 73, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  9. Bollobás B (2004) Extremal graph theory, dover edition. Dover Publications Inc., Mineola

    Google Scholar 

  10. Bonacich P (2004) The invasion of the physicists. Soc Netw 26:258–288

    Google Scholar 

  11. Borgatti SP, Mehra A, Brass DJ, Labianca G (2009) Network analysis in the social sciences. Science 323:892–895

    Article  Google Scholar 

  12. Borgatti SP, Halgin D (2011) The SAGE handbook of social network analysis. Analyzing affiliation networks. Sage Publications, London, pp 417–433

    Google Scholar 

  13. Cano P (2012) Music recommendation networks. In: Book of abstracts of the 3rd Leonardo satellite symposium on arts, humanities, and complex networks

    Google Scholar 

  14. Csárdi G, Nepusz T (2006) The igraph software package for complex network research. InterJournal Complex Systems:CX.18–1695

    Google Scholar 

  15. Csermely P (2009) Weak links: the universal key to the stability of networks and complex systems, 2nd edn. Springer, Heidelberg

    Book  MATH  Google Scholar 

  16. da Fontoura Costa L, Rodrigues FA, Travieso G, Villas Boas PR (2007) Characterization of complex networks: a survey of measurements. Adv Phys 56:167–242

    Article  Google Scholar 

  17. Dorogovtsev SN, Mendes JFF (2003) Evolution of networks. Oxford University Press

    Google Scholar 

  18. Easley D, Kleinberg J (2010) Networks, crowds, and markets: reasoning about a highly connected world. Cambridge University Press

    Google Scholar 

  19. Ebeling W, Sokolov IM. Statistical thermodynamics and stochastic theory of nonequilibrium systems. World Scientific Publishing Co. Pte. Ltd., Singapore

    Google Scholar 

  20. Erdős P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–61

    MathSciNet  MATH  Google Scholar 

  21. Euler L (1736) Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 8:128–140

    Google Scholar 

  22. Ferrer i Cancho R, Solé RV, (2001) The small world of human language. Proc R Soc Lond B 268:2261–2265

    Google Scholar 

  23. Freeman LC (2004) The development of social network analysis—a study in the sociology of science. Empirical Press, Vancouver

    Google Scholar 

  24. Freeman LC (2008) Going the wrong way on a one-way street: centrality in physics and biology. J Soc Struct 9(2):1–15

    MathSciNet  Google Scholar 

  25. Freeman LC (2011) The SAGE handbook of social network analysis. The development of social network analysis—with an emphasis on recent events. SAGE Publications Ltd., London, pp 26–39

    Google Scholar 

  26. Freeman LC, Freeman SC (1980) Electronic communication: technology and impacts. A semi-visible college: structural effects on a social networks group. Westview Press, Boulder, pp 77–85

    Google Scholar 

  27. Gigerenzer G (2002) Calculated risks: how to know when numbers deceive you. Simon & Schuster, New York

    Google Scholar 

  28. Gigerenzer G (2004) Mindless statistics. J Socio-Econ 33(5):587–606

    Article  Google Scholar 

  29. Gigerenzer G, Gaissmaier W, Kurz-Milcke E, Schwartz LM, Woloshin S (2007) Hel** doctors and patients make sense of health statistics. Psychol Sci Public Interest 8(2):electronic version: http://www.psychologicalscience.org/journals/pspi/pspi_8_2_article.pdf

    Google Scholar 

  30. Gigerenzer G, Krauss S, Vitouch O (2004) The SAGE handbook of quantitative methodology for the social sciences. The null ritual—what you always wanted to know about significance testing but were afraid to ask. SAGE Publications Ltd., London, pp 391–408

    Google Scholar 

  31. Goldenberg J, Libai B, Muller E, Stremersch S (2010) The evolving social network of marketing scholoars. Mark Sci 29:561–567

    Article  Google Scholar 

  32. Grannis R (2010) Six degrees of “who cares”. Amer J Sociol 115(4):991–1017

    Google Scholar 

  33. Hanneman R, Riddle M (2005) Introduction to social network methods. Online publication of the University of California, Riverside. http://faculty.ucr.edu/~hanneman/nettext/

  34. Hennig M, Brandes U, Pfeffer J, Mergel I (2012) Studying social networks—a guide to empirical research. Campus

    Google Scholar 

  35. Hodges DA, Burdette JH, Steen MR, Laurienti PJ, Wilkins RW (2011) Network science: a new method for investigating the complexity of musical experiences in the brain. In: Book of abstracts of the 2nd Leonardo satellite symposium on arts, humanities, and complex networks

    Google Scholar 

  36. Holland PW, Leinhardt S (1976) Local structure in social networks. Sociol Methodol 7:1–45

    Article  Google Scholar 

  37. Horvát EÁ, Hanselmann M, Hamprecht FA, Zweig KA (2012) One plus one makes three (for social networks). PLoS ONE 7(4):e34740

    Article  Google Scholar 

  38. Huang S (2004) Back to the biology in systems biology: what can we learn from biomolecular networks? Briefings Funct Genomics Proteomics 2(4):279–297

    Article  Google Scholar 

  39. Kolaczyk ED (2009) Statistical analysis of network data: methods and models. Springer, Heidelberg

    Book  MATH  Google Scholar 

  40. Lewis TG (2009) Network science: theory and applications. Wiley

    Google Scholar 

  41. Marin A, Wellman B (2011) The SAGE handbook of social network analysis. Social network analysis: an introduction. SAGE Publications Ltd., London, pp 12–25

    Google Scholar 

  42. Meeks E (2012) Orbis modeling transportation in the roman world. In: Book of abstracts of the 3rd Leonardo satellite symposium on arts, humanities, and complex networks

    Google Scholar 

  43. Moreno JL (1977) Who shall survive, 3rd edn. Beacon House Inc., New York

    Google Scholar 

  44. Newman ME (2010) Networks: an introduction. Oxford University Press, New York

    Book  MATH  Google Scholar 

  45. Onnela J-P, Saramäki J, Hvönen J, Szabó G, Lazer D, Kaski K, Kertész J, Barabási A-L (2007) Structure and tie strengths in mobile communication networks. Proc Natl Acad Sci 104:18

    Article  Google Scholar 

  46. Prell C (2011) Social network analysis. SAGE Publications Ltd., London

    Google Scholar 

  47. Rapoport A (1953) Spread of information through a population with socio-structural bias: I. Assumption of transitivity. Bull Math Biophys 15(4):523–533

    Article  MathSciNet  Google Scholar 

  48. Schelling TC (1978) Micromotives and macrobehavior. W.W. Norton & Company, New York

    Google Scholar 

  49. Scott J (2003) Social network analysis, 2nd edn, reprinted edition. SAGE Publications, London

    Google Scholar 

  50. Scott J, Carrington PJ (eds) (2011) The SAGE handbook of social network analysis. SAGE Publications Ltd., London

    Google Scholar 

  51. Scott J (2011) The SAGE handbook of social network analysis. Social physics and social networks. SAGE Publications Ltd., London, pp 55–66

    Google Scholar 

  52. Deutschland Statistisches Bundesamt (2013) Auszug aus dem Datenreport 2013—Private Haushalte - Einkommen, Ausgaben, Ausstattung. Electronic report at https://www.destatis.de/DE/Publikationen/Datenreport/Datenreport.html

  53. Sudarshan Iyengar SR, Zweig K, Natarajan A, Veni Madhavan CE (2011) A network analysis approach to understand human-wayfinding problem. In: Proceedings of the 33rd annual meeting of the cognitive science society

    Google Scholar 

  54. Sylvester JJ (1878) Chemistry and algebra. Nature 17:284

    Article  Google Scholar 

  55. http://cran.r-project.org/web/packages/sna/index.html

  56. http://networkx.github.io/

  57. https://gephi.org/

  58. Vicsek T (2002) The bigger picture. Nature 418:131

    Article  Google Scholar 

  59. Wasserman S, Faust K (1999) Social network analysis—methods and applications, revised, reprinted edition. Cambridge University Press, Cambridge

    Google Scholar 

  60. Watts DJ (1999) Small worlds—the dynamics of networks between order and randomness. Princeton Studies in Complexity, Princeton University Press

    Google Scholar 

  61. Watts DJ (2003) Six degrees—the science of a connected age. W.W. Norton & Company, New York

    Google Scholar 

  62. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442

    Article  Google Scholar 

  63. www.cytoscape.org

Download references

Author information

Authors and Affiliations

  1. TU Kaiserslautern, FB Computer Science, Graph Theory and Analysis of Complex Networks, Gottlieb-Daimler-Str. 48, 67331, Kaiserslautern, Germany

    Katharina A. Zweig

Authors
  1. Katharina A. Zweig
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Katharina A. Zweig .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag GmbH Austria

About this chapter

Cite this chapter

Zweig, K.A. (2016). Graph Theory, Social Network Analysis, and Network Science. In: Network Analysis Literacy. Lecture Notes in Social Networks. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0741-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-0741-6_2

  • Published:

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-0740-9

  • Online ISBN: 978-3-7091-0741-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation