On the Eigenvalue Power Law

  • Milena Mihail
  • Christos Papadimitriou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)


We show that the largest eigenvalues of graphs whose highest degrees are Zipf-like distributed with slope a are distributed according to a power law with slope α/2. This follows as a direct and almost certain corollary of the degree power law. Our result has implications for the singular value decomposition method in information retrieval.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Milena Mihail
    • 1
  • Christos Papadimitriou
    • 2
  1. 1.College of ComputingGeorgia Institute of TechnologyAtlanta
  2. 2.Computer Science DepartmentBerkeley

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