Application of Semidefinite Programming to Maximize the Spectral Gap Produced by Node Removal

Conference paper

DOI: 10.1007/978-3-642-36844-8_15

Part of the Studies in Computational Intelligence book series (SCI, volume 476)
Cite this paper as:
Masuda N., Fujie T., Murota K. (2013) Application of Semidefinite Programming to Maximize the Spectral Gap Produced by Node Removal. In: Ghoshal G., Poncela-Casasnovas J., Tolksdorf R. (eds) Complex Networks IV. Studies in Computational Intelligence, vol 476. Springer, Berlin, Heidelberg

Abstract

The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.

Keywords

combinatorial optimization network synchronization random walk opinion formation Laplacian eigenvalue 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematical InformaticsThe University of TokyoBunkyoJapan
  2. 2.PRESTOJapan Science and Technology AgencyKawaguchiJapan
  3. 3.Graduate School of BusinessUniversity of HyogoNishi-kuJapan

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