The Linear Algebra of Graphs



Graphs are encountered in many real-world settings, such as the Web, social networks, and communication networks. Furthermore, many machine learning applications are conceptually represented as optimization problems on graphs. Graph matrices have a number of useful algebraic properties, which can be leveraged in machine learning. There are close connections between kernels and the linear algebra of graphs; a classical application that naturally belongs to both fields is spectral clustering (cf. Section 10.5).


  1. 9.
    A. Azran. The rendezvous algorithm: Multiclass semi-supervised learning with markov random walks. ICML, pp. 49–56, 2007.Google Scholar
  2. 17.
    S. Bhagat, G. Cormode, and S. Muthukrishnan. Node classification in social networks. Social Network Data Analytics, Springer, pp. 115–148. 2011.Google Scholar
  3. 24.
    S. Brin, and L. Page. The anatomy of a large-scale hypertextual web search engine. Computer Networks, 30(1–7), pp. 107–117, 1998.Google Scholar
  4. 25.
    A. Brouwer and W. Haemers. Spectra of graphs. Springer Science and Business Media, 2011.Google Scholar
  5. 29.
    F. Chung. Spectral graph theory. American Mathematical Society, 1997.zbMATHGoogle Scholar
  6. 40.
    D. Easley, and J. Kleinberg. Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge University Press, 2010.CrossRefGoogle Scholar
  7. 43.
    M. Faloutsos, P. Faloutsos, and C. Faloutsos. On power-law relationships of the internet topology. ACM SIGCOMM Computer Communication Review, pp. 251–262, 1999.Google Scholar
  8. 82.
    B. London and L. Getoor. Collective classification of network data. Data Classification: Algorithms and Applications, CRC Press, pp. 399–416, 2014.Google Scholar
  9. 84.
    U. von Luxburg. A tutorial on spectral clustering. Statistics and computing, 17(4), pp. 395–416, 2007.MathSciNetCrossRefGoogle Scholar
  10. 98.
    A. Ng, M. Jordan, and Y. Weiss. On spectral clustering: Analysis and an algorithm. NIPS Conference, pp. 849–856, 2002.Google Scholar
  11. 115.
    J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), pp. 888–905, 2000.CrossRefGoogle Scholar
  12. 138.
    R. Zafarani, M. A. Abbasi, and H. Liu. Social media mining: an introduction. Cambridge University Press, 2014.CrossRefGoogle Scholar
  13. 143.
    X. Zhu, Z. Ghahramani, and J. Lafferty. Semi-supervised learning using gaussian fields and harmonic functions. ICML Conference, pp. 912–919, 2003.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations