Skip to main content
SpringerLink
Log in

Graphs and Matrices

  • Chapter
  • First Online:
Book cover Mathematical Tools for Data Mining

Part of the book series: Advanced Information and Knowledge Processing ((AI&KP))

  • 3590 Accesses

Abstract

Graphs model relations between elements of sets. The term “graph” is suggested by the fact that these mathematical structures can be graphically represented.

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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. D.J. Cook, L.B. Holder, Mining Graph Data (Wiley-Interscience, Hoboken, 2007)

    MATH  Google Scholar 

  2. C. Aggarwal, H. Wang (eds.), Managing and Mining Graph Data (Springer, New York, 2010)

    MATH  Google Scholar 

  3. V. Havel, A remark on the existence of finite graphs. Čas. pro Pěst. Mat. 80, 477–480 (1955)

    MATH  MathSciNet  Google Scholar 

  4. S.L. Hakimi, On the realizability of a set of integers as degrees of the vertices of a graph. SIAM J. Appl. Math. 10, 496–506 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Rymon, Search through systematic set enumeration, in Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, MA, ed. by B. Nebel, C. Rich, W.R. Swartout (Morgan Kaufmann, San Mateo, CA, 1992), pp. 539–550

    Google Scholar 

  6. H. Prüfer, Neuer beweis eines satzes über permutationen. Archiv für Mathematik und Physik 27, 142–144 (1918)

    MATH  Google Scholar 

  7. M. Fiedler, Special Matrices and Their Applications in Numerical Mathematics, 2nd edn. (Dover Publications, New York, 2008)

    MATH  Google Scholar 

  8. A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Academic Press, New York, 1979)

    MATH  Google Scholar 

  9. F. Harary, Graph Theory (Addison-Wesley, Reading, 1971)

    Google Scholar 

  10. C. Berge, The Theory of Graphs (Dover, New York, 2001)

    MATH  Google Scholar 

  11. B. Bollobás, Graph Theory—An Introductory Course (Springer-Verlag, New York, 1979)

    MATH  Google Scholar 

  12. R. Diestel, Graph Theory (Springer-Verlag, Berlin, 2005)

    MATH  Google Scholar 

  13. R.E. Tarjan, Data Structures and Network Algorithms (SIAM, Philadelphia, 1983)

    Book  Google Scholar 

  14. O. Ore, Arc coverings of graphs. Ann. Mat. Pura Appl. 55, 315–322 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  15. O. Ore, Hamilton connected graphs. J. Math. Pures Appl. 42, 21–27 (1963)

    MATH  MathSciNet  Google Scholar 

  16. G.A. Dirac, Some theorems on abstract graphs. Proc. London Math. Soc. 2, 69–81 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  17. V. Chvátal, P.L. Hammer, Aggregation of inequality in integer programming. Ann. Discrete Math. 1, 145–162 (1977)

    Article  Google Scholar 

  18. J. Matoušek, J. Neštřil, Invitation to Discrete Mathematics, 2nd edn. (Oxford University Press, Oxford, 2011)

    Google Scholar 

  19. D. Cvetković, Graphs and their spectra. Publ. Elek. Fak. Univ. Beograd: Ser. Mat. Fiz. 354, 1–50 (1971)

    Google Scholar 

  20. A.E. Brouwer, W.H. Haemers, Spectra of Graphs (Springer, New York, 2011)

    Google Scholar 

  21. R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985)

    Book  MATH  Google Scholar 

  22. A.N. Langville, C.D. Meyer, Google’s Page Rank and Beyond: The Science of Search Engine Rankings (Princeton University Press, Princeton, 2006)

    Google Scholar 

  23. A. Bonato, A Course on the Web Graph (American Mathematical Society, Providence, 2008)

    MATH  Google Scholar 

  24. F. Harary, The determinant of the adjacency matrix of a graph. SIAM Rev. 4, 202–210 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  25. L. Lovasz, M.D. Plummer, Matching Theory (American Mathematical Society, Providence, 2009)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Massachusetts Boston, Boston, MA, USA

    Dan A. Simovici

  2. University Lille 1, Laboratoire d’Informatique Fundamentale de Lille, Villeneuve d’Ascq, France

    Chabane Djeraba

Authors
  1. Dan A. Simovici
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chabane Djeraba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan A. Simovici .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this chapter

Cite this chapter

Simovici, D.A., Djeraba, C. (2014). Graphs and Matrices. In: Mathematical Tools for Data Mining. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-1-4471-6407-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-6407-4_10

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-6406-7

  • Online ISBN: 978-1-4471-6407-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation