On the Eigenvalue Power Law

  • Milena Mihail
  • Christos Papadimitriou
Conference paper

DOI: 10.1007/3-540-45726-7_20

Volume 2483 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Mihail M., Papadimitriou C. (2002) On the Eigenvalue Power Law. In: Rolim J.D.P., Vadhan S. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 2002. Lecture Notes in Computer Science, vol 2483. Springer, Berlin, Heidelberg

Abstract

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