Chapter

Randomization and Approximation Techniques in Computer Science

Volume 2483 of the series Lecture Notes in Computer Science pp 254-262

Date:

On the Eigenvalue Power Law

  • Milena MihailAffiliated withCollege of Computing, Georgia Institute of Technology
  • , Christos PapadimitriouAffiliated withComputer Science Department

* Final gross prices may vary according to local VAT.

Get Access

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.